Question 6
6
7 marks
Question 6(a)
6(a)
Explain what is meant by a photon.
Easystructured2 marks
Answer
packet/quantum/discrete amount of energy of electromagnetic energy/radiation/waves A1
Question 6(b)
6(b)
An X-ray photon of energy \(3.06 \times 10^{-14} \mathrm{~J}\) is incident on an isolated stationary electron, as illustrated in Fig. 6.1. The photon is deflected elastically by the electron through angle \(\theta\). The deflected photon has a wavelength of \(6.80 \times 10^{-12} \mathrm{~m}\).
structured3 marks
Question 6(b)(ii)
6(b)(ii)
Calculate 1. the energy of the deflected photon, 2. the speed of the electron after the photon has been deflected. \(\mathrm{m} \mathrm{s}^{-1}[3]\)
Hardstructured3 marks
Answer
1. \(E=h c / \lambda\) 2. energy of electron \(=(3.06-2.93) \times 10^{-14}\) speed \(=\sqrt{(2 E / m)}\)
Question 6(c)
6(c)
Explain why the magnitude of the final momentum of the electron is not equal to the change in magnitude of the momentum of the photon.
Hardstructured2 marks
Answer
momentum is a vector quantity either must consider momentum in two directions or direction changes so cannot just consider magnitude
Question 8
8
White light is incident on a cloud of cool hydrogen gas, as illustrated in Fig. 8.1. The spectrum of the light emerging from the gas cloud is found to contain a number of dark lines.
structured4 marks
Question 8(b)
8(b)
Some electron energy levels in a hydrogen atom are illustrated in Fig. 8.2. One dark line is observed at a wavelength of 435 nm .
structured4 marks
Question 8(b)(i)
8(b)(i)
Calculate the energy, in eV , of a photon of light of wavelength 435 nm .
Mediumstructured4 marks
Answer
\(E=h c / \lambda\) C1 \(\begin{array}{ll}=\left(6.63 \times 10^{-34} \times 3 \times 10^{8}\right) /\left(435 \times 10^{-9}\right) & \mathrm{C} 1 \\ =4.57 \times 10^{-19} \mathrm{~J} \text { (allow } 2 \text { s.f.) } & \mathrm{C} 1\end{array}\) \(=\left(4.57 \times 10^{-19}\right) /\left(1.6 \times 10^{-19}\right)(\mathrm{eV})\) =2.86 eV (allow 2 s.f.) A1 [4]
Question 8
8
Light of wavelength 590 nm is incident normally on a surface, as illustrated in Fig. 8.1. The power of the light is 3.2 mW . The light is completely absorbed by the surface.
structured4 marks
Question 8(a)
8(a)
Calculate the number of photons incident on the surface in 1.0 s .
Mediumstructured0 marks
Answer
photon energy \(=h c / \lambda\)
Question 8(b)
8(b)
Use your answer in (a) to determine
structured4 marks
Question 8(b)(i)
8(b)(i)
the total momentum of the photons arriving at the surface in 1.0 s , \(\mathrm{kgms}^{-1}\)
Mediumstructured3 marks
Answer
\(p=h / \lambda \quad \mathrm{C} 1\)
Question 8(b)(ii)
8(b)(ii)
the force exerted on the surface by the light.
Mediumstructured1 marks
Answer
force \(=1.06 \times 10^{-11} \mathrm{~N}\)
Question 8
8
A photon of wavelength \(6.50 \times 10^{-12} \mathrm{~m}\) is incident on an isolated stationary electron, as illustrated in Fig. 8.1. The photon is deflected elastically by the electron of mass \(m_{\mathrm{e}}\). The wavelength of the deflected photon is \(6.84 \times 10^{-12} \mathrm{~m}\).
structured7 marks
Question 8(a)
8(a)
Calculate, for the incident photon,
structured2 marks
Question 8(a)(i)
8(a)(i)
its momentum, momentum = Ns
Easystructured2 marks
Answer
\(p=h / \lambda\)
Question 8(a)(ii)
8(a)(ii)
its energy. energy =
Easystructured0 marks
Answer
\(E=h c / \lambda\) or E=p c
Question 8(b)
8(b)
The angle \(\theta\) through which the photon is deflected is given by the expression where \(\Delta \lambda\) is the change in wavelength of the photon, h is the Planck constant and c is the speed of light in free space.
structured5 marks
Question 8(b)(i)
8(b)(i)
Calculate the angle \(\theta\).
Hardstructured2 marks
Answer
\(0.34 \times 10^{-12}=\left(6.63 \times 10^{-34}\right) /\left(9.11 \times 10^{-31} \times 3.0 \times 10^{8}\right) \times(1-\cos \theta) \quad\) C1
Question 8(b)(ii)
8(b)(ii)
Use energy considerations to suggest why \(\Delta \lambda\) must always be positive.
Hardstructured3 marks
Answer
deflected electron has energy ..... M1 this energy is derived from the incident photon ..... A1 deflected photon has less energy, longer wavelength (so \(\Delta \lambda\) always positive) ..... B1 [3]
Question 8
8
The power for a space probe is to be supplied by the energy released when plutonium- 236 decays by the emission of \(\alpha\)-particles. The \(\alpha\)-particles, each of energy 5.75 MeV , are captured and their energy is converted into electrical energy with an efficiency of 24 %.
structured1 marks
Question 8(a)
8(a)
Calculate
structured1 marks
Question 8(a)(i)
8(a)(i)
the energy, in joules, equal to 5.75 MeV , energy = J
Easystructured1 marks
Answer
energy \(=5.75 \times 1.6 \times 10^{-13}\)
Question 8
8
\(8 \mathrm{~A} \pi^{0}\) meson is a sub-atomic particle. A stationary \(\pi^{0}\) meson, which has mass \(2.4 \times 10^{-28} \mathrm{~kg}\), decays to form two \(\gamma\)-ray photons. The nuclear equation for this decay is
structured2 marks
Question 8(b)
8(b)
Determine, for each \(\gamma\)-ray photon,
structured2 marks
Question 8(b)(i)
8(b)(i)
the energy, in joule, energy = J
Mediumstructured2 marks
Answer
\(\begin{array}{rlr}(\Delta) E & =(\Delta) m c^{2} & \text { C1 } \\ & =1.2 \times 10^{-28} \times\left(3.0 \times 10^{8}\right)^{2} & \end{array}\)
Question 8(b)(iii)
8(b)(iii)
the momentum. Answer all the questions in the spaces provided.
Mediumstructured0 marks
Answer
\(\lambda=h / p\) \(p=\left(6.63 \times 10^{-34}\right) /\left(1.84 \times 10^{-14}\right) \quad \mathrm{C} 1\) C1 C1 A1 8 M1 A1 [2] 1 A1 Section B