Atomic and Nuclear Physics Answers

 (a) A radioactive nucleus 180 72 X undergoes a series of radioactive α, β−, α, γ radiations and successively decays into X1, X2, X3 and X4. What are A and Z of the final nucleus X4.

(b) What is pair production? Explain why pair production cannot occur bellow an energy of 1.02MeV .

(c) Consider the following nuclear reactions. Classify all the elementary particles involved and tell which of the two reactions is allowed / not allowed and explain why?.

i. p + ¯νe −→ n + µ + ii. p + ¯νe −→ n + e + (d) How much time (in years) will be required for 5 mg of 22Na (T1/2 = 2.60yrs) to reduce to 1 mg?.

In the Helium-Neon laser, lasing occurs between two excited states of the neon atom. However, in many lasers lasing occurs between the ground state and an excited state. Consider such a laser that emits at wavelength λ = 550 nm. If a population inversion is not generated, (i) what is the ratio of the population of atoms in state Ex to the population in the ground state E0 with atoms at room temperature? For the condition in (i), at (ii) what temperature would the ratio Nx/N0 be 1/2?.

How much energy (in Joules) will be produced on complete fission of 1 kg of Uranium (235U), considering that only 0.1% of mass is converted into energy.

3. (i) In the presence of an external uniform magnetic field, the normal Zeeman effect is observed

and the original transition generates into three transitions of frequencies:

ν = ν0 −



eB

4πm

; ν = ν0; ν = ν0 +



eB

4πm

where m is the mass of the electron. Using a diagram, indicate what are allowed normal

Zeeman transitions between d(l = 2) state and p(l = 1) state. [6 marks]

(ii) Find the minimum magnetic field needed for the Zeeman effect to be observed in a

spectral line of 400 nm wavelength when a spectrometer whose resolution is 0.010 nm is

used.

(a) Compute the energy released from a pair production reaction. [2 marks]

(b) Using the line of stability curve, briefly explain why Helium 6

2He is unstable and would

eventually decay into 6

3Li. Indicate the corresponding decay reaction equation. [4 marks]

(c) The Figure bellow represents a typical X-ray spectrum from a tungsten target. Explain the

behaviour of the observed spectrum as far the mechanism of X-ray production is concerned.

[4 marks] .

Determine approximately the ratio of the probability of spontaneous emission

to the probability of stimulated emission at room temperature in (a) X-ray

region of the EM spectrum (b) the visible region (c) the microwave region.

Determine approximately the ratio of the probability of spontaneous emission

to the probability of stimulated emission at room temperature in (a) X-ray

region of the EM spectrum (b) the visible region (c) the microwave region.

Using the concept of QM you have learned (application of the SE to H-like atoms), derive / discuss the (existence of ) quantum numbers n, l, ml

One of the most prominent spectral lines of Calcium is the one with wavelength 𝜆 = 4226.73 𝐴 𝑜 [transition from 𝑝(𝑙 = 1) to 𝑠(𝑙 = 0)]. Calcium atoms exhibit normal Zeeman patterns when placed in a uniform magnetic field of 4 𝑇𝑒𝑠𝑙𝑎. Calculate the wavelength of the three components of a normal Zeeman pattern and the separation between them. 

On 20 July 1969, the astronauts of Apollo 11 placed a reflector on the surface of the moon that with the telescope and electronic equipment on earth allows measurements of the time of flight of laser pulses from earth to the moon and back. Scientists are able to measure the time of flight of laser pulse from earth to the moon and back with an accuracy of one nanosecond. What is the accuracy of the distance to the moon distance?