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*Answer can only contain numeric values

QUESTION: 1

A stone with mass 1kg is whirled in a horizontal circle of radius 1m with a period of revolution equal to 1s. What value of orbital angular momentum quantum no. l describes this motion? (in 10^{34})

Solution:

The speed of the stone in its orbit is

Angular momentum = ** mvr =** 1

= 6.28

For classical objects the quantum numbers are excessively big

The correct answer is: 5.96

*Answer can only contain numeric values

QUESTION: 2

Calculate the minimum value of for the stone mentioned in problem 4.

Solution:

The correct answer is: 0.9964

*Answer can only contain numeric values

QUESTION: 3

Calculate the average distance of an electron from the nucleus in the ground state of hydrogen atom is unit of a_{0}.

Solution:

The correct answer is: 1.5

*Answer can only contain numeric values

QUESTION: 4

Find the level of degeneracy for particle in a 3** d** box with energy

Solution:

level of degeneracy = 6

The correct answer is: 6

*Answer can only contain numeric values

QUESTION: 5

Find the value of the normalisation constant in the unit of that normalizes the ground state wavefunction of the particle in a box of lengths L, 2L, 3L in x, y and z directions respectively. Take √3 = 1.732

Solution:

The probability density Integration over the volume of the cube must be unity

The correct answer is: 1.15

*Answer can only contain numeric values

QUESTION: 6

Find the level of degeneracy for a 3 dimensional isotropic quantum harmonic oscillator of energy

Solution:

(0, 0, 8) 3 states

(2, 2, 4) 3 states

(3, 3, 2) 3 states

(1, 1, 6) 3 states

(4, 4, 0) 3 states

= 3 × 5 = 15 states

Rest will give 6 states each

(0, 1, 7)(1, 2, 5)(4, 1, 3)(2, 0, 6)(0, 3, 5)

6 × 5 = 30

Total = 15 + 30 = 45 states

The correct answer is: 45

*Answer can only contain numeric values

QUESTION: 7

Consider two harmonic oscillators in 3 dimensions. For what ratio of angular frequencies will the first excited state of one oscillator have energy twice that of the second oscillator’s third excited state energy i.e find

Solution:

The correct answer is: 3.6

*Answer can only contain numeric values

QUESTION: 8

Modeling a defect trap in a crystal as a 3** d** box with edge length 5

Solution:

= 0.0716 × 10^{-68 + 31 + 20}

= 0.0714 × 10^{-17} **Joules**

= 0.0447 × 10^{2} **eV**

= 4.5 **eV**

The correct answer is: 4.5

*Answer can only contain numeric values

QUESTION: 9

Find the probability of finding a particle in a 3** d** box of length

(Assume the particle to be in the ground state).

Solution:

= 0.04

The correct answer is: 0.04

*Answer can only contain numeric values

QUESTION: 10

Calculate the probability that the electron in the ground state of hydrogen will be found outside the first Bohr radius in the unit ** e^{–2}**. Take

Solution:

The probability is found by integrating the radial probability density for this state from *a*_{0} to ∞.

The correct answer is: 5

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