4.(a) What is deuterium and who discovered it? (b) What did the Stern-Gerlach ex

Question

4.(a) What is deuterium and who discovered it? (b) What did the Stern-Gerlach experiment show? label (c) How many magnets did the Stern-Gerlach experiment use? How many were needed in Rabi's refocusing method of the mid-1930s and how many magnets are there in the magnetic resonance apparatus of Rabi? distance 7. (a) In Figure C which shows calculations for a particle in a one dimensional box. label the two graphs. What functions do they show? (b) List the points in the box where the particle will never be found. (c) List the points in the box where the particle is most likely to be found. distance in x Figure D (d) In terms of L (size of box), h (Planck's constant), m(particle mass) what is the energy of the particle in the box of figure C. 8. (a) How many dimensions does the box in figure D, with one particle in it, have? (b) How many quantum numbers are necessary to specify the state of the particle in the box of figure D Figure E (c) Specify the quantum numbers of the particle in the box of figure D.

Explanation / Answer

8a]

There are two dimensions available for the particle. This is because the probability amplitude is non-zero in both x and y directions.

b] Since each dimension has its independent energy quantization, therefore the number of quantum numbers needed to specify the state of the particle in the box is 2.

c] Because there are two lobes along y direction and none in x direction, the quantum numbers will be:

since number of lobes = (m+1)(n+1)

where m and n are the quantum numbers

therefore,

2 = (0+1)(n+1)

=> n = 1

so, m = 0 and n = 1.

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