A quantum particle of mass m is confined to a square region in XOY-plane whose vertices are given by (0, 0), (L, 0), (L, L) and (0, L). Which of the following represents an admissible wave function of the particle (for I, m, n positive integers)?

A particle of mass m is confined in the potential
Quantum Mechanics mcq question image

\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

A

$$\frac{{31}}{{10}}\hbar \omega $$

B

$$\frac{{25}}{{10}}\hbar \omega $$

C

$$\frac{{13}}{{10}}\hbar \omega $$

D

$$\frac{{11}}{{10}}\hbar \omega $$

A particle of mass m is confined in an infinite potential well \[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0,}&{{\text{if }}0 It is subjected to a perturbing potential $${V_P}\left( x \right) = {V_0}\sin \left( {\frac{{2\pi x}}{L}} \right)$$ within the well. Let E⁽¹⁾ and E⁽²⁾ be the corrections to the ground state energy in the first and second order in V₀.
Quantum Mechanics mcq question image

Which of the following is correct?

A

[

A. E⁽¹⁾ = 0; E⁽²⁾

B. E⁽¹⁾ > 0; E⁽²⁾ = 0

B

E⁽¹⁾ = 0; E⁽²⁾ depends on the sign of V₀

C

E⁽¹⁾ (2)

Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm

A

Quantity 2 > Quantity 3 > Quantity 1

B

Quantity 1 > Quantity 2 > Quantity 3

C

Quantity 3 > Quantity 1 > Quantity 2

D

Quantity 1 = Quantity 2 < Quantity 3

E

Quantity 1 > Quantity 2 = Quantity 3

Which of the following is are true about progressive waves (i) No particle of the medium is completely at rest (ii) Energy is confined to a region (iii) There is a continuous change of phase from one particle to next (iv) The disturbance which produces wave is confined to the region where it is produced

A

(i) & (ii)

B

(i), (ii) & (iii)

C

(i) & (iii)

D

(i) & (iv)

Which of the following statements concerning the quantum numbers is correct? (i) The Angular quantum number determines the three-dimensional shape of the orbital. (ii) The Principal quantum number determines the orientation and energy of the orbital. (iii) The Magnetic quantum number determines the size of the orbital. (iv) Spin quantum number of an electron determines the orientation of the spin of the electron relative to the chosen axis.

A

ii and iv

B

i and iv

C

i and iii

D

ii and iii

A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.
Quantum Mechanics mcq question image

The wave functions in regions I and II are respectively

A

decaying, oscillatory

B

oscillatory, oscillatory

C

oscillatory, decaying

D

decaying, decaying

A particle with energy E is in a time independent double well potential as shown in the figure. Which, of the following statements about the particle is not correct?
Quantum Mechanics mcq question image

A

The particle will always be in a bound state

B

The probability of finding the particle in one well will be time dependent

C

The particle will be confined to anyone of the wells

D

The particle can tunnel from one well to the other and back

What is the monoisotopic and average mass of valine? Given data: Mass of the most abundant isotope of Carbon (C°)=12.0000, Mass of most abundant isotope of Hydrogen (H°)=1.0078, Mass of most abundant isotope of Oxygen (O°)=15.9949, Mass of most abundant isotope of Nitrogen (N°)=14.0031, The average mass of Carbon (C)=12.011, The average mass of Hydrogen (H)=1.008, The average mass of Oxygen (O)=15.999, The average mass of Nitrogen (N)=14.007.

A

99.068 and 99.2361

B

99.216 and 99.326

C

99.111 and 99.321

D

99.068 and 99.132

In the following figure, the circle represents integers, the triangle represents vowels, the rectangle represents alphabets, and the pentagon represents consonants. Which of the following numbers represents alphabets that are integers.

A

24

B

48

C

30

D

27

A, B, C, D and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 4. D is the greatest and A is the least. B is greater than E but less than C. The sum of the integers is equal to E. What is the positive difference between the lowest and the highest integers?

A

8

B

6

C

16

D

18

A quantum particle of mass m is confined to a square region in XOY-plane whose vertices are given by (0, 0), (L, 0), (L, L) and (0, L). Which of the following represents an admissible wave function of the particle (for I, m, n positive integers)?

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