DP Physics Questionbank

The graph shows the variation of photoelectric current I with potential difference V between C and A when violet light of a particular intensity is used.

The intensity of the light source is increased without changing its wavelength.

(i) Draw, on the axes, a graph to show the variation of I with V for the increased intensity.

(ii) The wavelength of the violet light is 400 nm. Determine, in eV, the work function of caesium.

(iii) V is adjusted to +2.50V. Calculate the maximum kinetic energy of the photoelectrons just before they reach A.

C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in the dead tree is determined to have fallen to 21% of its original value. C-14 has a half-life of 5700 years.

(i) Explain why the activity of C-14 in the dead tree decreases with time.

(ii) Calculate, in years, the age of the dead tree. Give your answer to an appropriate number of significant figures.

A current is observed on the ammeter when violet light illuminates C. With V held constant the current becomes zero when the violet light is replaced by red light of the same intensity. Explain this observation.

An electron of mass m has an uncertainty in its position r. What is the uncertainty in the speed of this electron?

A. $\frac{h}{4\pi r}$

B. $\frac{hr}{4\pi m}$

C. $\frac{hm}{4\pi r}$

D. $\frac{h}{4\pi mr}$

The diameter of a silver-108 (${}_{47}^{108}Ag$) nucleus is approximately three times that of the diameter of a nucleus of

A.  ${}_2^{4}He.$

B.  ${}_3^{7}Li.$

C.  ${}_5^{11}B.$

D.  ${}_{10}^{20}Ne.$

In the Bohr model for hydrogen an electron in the ground state has orbit radius r and speed v. In the first excited state the electron has orbit radius 4r. What is the speed of the electron in the first excited state?

A.  $\frac{v}{2}$

B.  $\frac{v}{4}$

C.  $\frac{v}{8}$

D.  $\frac{v}{16}$

Determine a value for Planck’s constant.

What can be used to calculate the probability of finding an electron in a particular region of space?

A.  $\frac{\text{Planck's constant}}{4\pi \times \text{uncertainty in energy}}$

B.  $\frac{\text{Planck's constant}}{4\pi \times \text{uncertainty in speed}}$

C.  The magnitude of the wave function

D.  The magnitude of the (wave function)²

A neutron of mass m is confined within a nucleus of diameter d. Ignoring numerical constants, what is an approximate expression for the kinetic energy of the neutron?

A.  $\frac{h^2}{m{d}^2}$

B.  $\frac{h}{md}$

C.  $\frac{m{h}^2}{d^2}$

D.  $\frac{h}{m^{2}d}$

Show that about 3 x 10¹⁵ alpha particles are emitted by the radium-226 in 6 days.

A radioactive element has decay constant $\lambda$ (expressed in s^–1). The number of nuclei of this element at t = 0 is N. What is the expected number of nuclei that will have decayed after 1 s?

A.  $N\left(1-e^{-\lambda }\right)$

B.  $\frac{N}{\lambda }$

C.  $N{e}^{-\lambda }$

D.  $\lambda N$

Deduce that the activity of the radium-226 is almost constant during the experiment.

Calculate the wavelength of the light.

Radiation of photon energy 5.2 x 10^–19 J is now incident on the photocell. Calculate the maximum velocity of the emitted electrons.

State and explain the effect on the maximum photoelectric current as a result of increasing the photon energy in this way.

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Outline why the particles must be accelerated to high energies in scattering experiments.

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph shows the relationship between the half-life $t_{\frac{1}{2}}$ and the activity A for the samples?

Plot the position of magnesium-24 on the graph.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

A particle of energy $E$ is incident upon a barrier and has a certain probability of quantum tunnelling through the barrier. Assuming $E$ remains constant, which combination of changes in particle mass and barrier length will increase the probability of the particle tunnelling through the barrier?

An electron of non-relativistic speed $v$ interacts with an atom. All the energy of the electron is transferred to an emitted photon of frequency $f$ . An electron of speed $2v$ now interacts with the same atom and all its energy is transmitted to a second photon. What is the frequency of the second photon?

A.  $\frac{f}{4}$

B.  $\frac{f}{2}$

C.  $2f$

D.  $4f$

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. At time t = 0 samples of X and Y contain the same number of nuclei.

What is $\frac{\text{number of nuclei of X undecayed}}{\text{number of nuclei of Y undecayed}}$ when t = 200 s?

A.     4

B.     2

C.     $\frac{1}{2}$

D.     $\frac{1}{4}$

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

Show that the energy of photons from the UV lamp is about 10 eV.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

Two samples X and Y of different radioactive isotopes have the same initial activity. Sample X has twice the number of atoms as sample Y. The half-life of X is T. What is the half-life of Y?

A.     2T

B.     T

C.     $\frac{T}{2}$

D.     $\frac{T}{4}$

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

Calculate the electron’s orbital radius in (c)(ii).

Explain what may be deduced about the energy of the electron in the β^– decay.

Calculate the wavelength of the gamma ray photon in (d)(ii).

In a photoelectric experiment a stopping voltage $V$ required to prevent photoelectrons from flowing across the photoelectric cell is measured for light of two frequencies $f_1$ and $f_2$. The results obtained are shown.

The ratio $\frac{V_2-V_1}{f_2-f_1}$ is an estimate of

A.  $e$

B.  $h$

C.  $\frac{e}{h}$

D.  $\frac{h}{e}$

A beam of electrons moving in the direction shown is incident on a rectangular slit of width $d$.

The component of momentum of the electrons in direction $y$ after passing through the slit is $p$. The uncertainty in $p$ is

A.  proportional to $d$

B.  proportional to $\frac{1}{d}$

C.  proportional to $\frac{1}{d^2}$

D.  zero

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

Estimate the power, in kW, that is available from the plutonium at launch.

The spacecraft will take 7.2 years (2.3 × 10⁸ s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.

The graph shows the variation of the natural log of activity, ln (activity), against time for a radioactive nuclide.

What is the decay constant, in days^–1, of the radioactive nuclide?

A.   $\frac{1}{6}$

B.   $\frac{1}{3}$

C.   3

D.   6

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

Light with photons of energy 8.0 × 10⁻²⁰J are incident on a metal surface in a photoelectric experiment.

The work function of the metal surface is 4.8 × 10⁻²⁰J . What minimum voltage is required for the ammeter reading to fall to zero?

A.  0.2 V

B.  0.3 V

C.  0.5 V

D.  0.8 V

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.

The half-life of potassium-40 is 1.3 × 10⁹ years. Estimate the age of the rock sample.

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Which graph shows a possible probability density function ${\left|\text{Ψ}\right|}^2=\frac{P\left(r\right)}{\Delta V}$ for a given wave function $\text{Ψ}$ of an electron?

The dashed line represents the variation with incident electromagnetic frequency $f$ of the kinetic energy E_K of the photoelectrons ejected from a metal surface. The metal surface is then replaced with one that requires less energy to remove an electron from the surface.

Which graph of the variation of E_K with $f$ will be observed?

Estimate, using the result in (a)(iii), the volume of a tin-118 $\left({}_{50}{}^{118}\text{Sn}\right)$ nucleus. State your answer to an appropriate number of significant figures.

The de Broglie wavelength for an electron is given by $\frac{hc}{E}$. Show that the diameter of an oxygen-16 nucleus is about 4 fm.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

A beam of monochromatic radiation is made up of photons each of momentum $p$. The intensity of the beam is doubled without changing frequency. What is the momentum of each photon after the change?

A.  $\frac{p}{2}$

B.  $p$

C.  $2p$

D.  $4p$

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

Calculate, in eV, the work function of the metal surface.