Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be

A vibrational-electronic spectrum of homonuclear binary molecules, involving electronic ground state ε'' and excited ε', exhibits a continuum at $$\overline v $$ cm^-1. If the total energy of the dissociated atoms in the excited state exceeds the total energy of the dissociated atoms in the ground state by E_ex cm^-1, then dissociation energy of the molecule in the ground state is

A

$$\frac{{\left( {\overline v + {E_{ex}}} \right)}}{2}$$

B

$$\frac{{\left( {\overline v - {E_{ex}}} \right)}}{2}$$

C

$$\left( {\overline v - {E_{ex}}} \right)$$

D

$$\sqrt {\left( {\overline v - {E_{ex}}^2} \right)} $$

A particle of mass m is confined in the potential

\[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

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

উত্তেজিত অবস্থায় হাইড্রওজেন পরমাণুর কোয়ান্টাম সংখ্যা n=4 I=1 বিশিষ্ট অর্বিটালটি কি? (What is the orbital of hydrogen atom at its excited state with quantum number, n = 4, l = 1?)

A

s orbital

B

p orbital

C

dz2 orbital

D

dx2-y2

উত্তেজিত অবস্থায় হাইড্রোজেন পরমাণুর কোয়ান্টাম সংখ্যা n= 4, l= 1 বিশিষ্ট অর্বিটালটি কি? (What is the orbital of hydrogen atom at its excited state with quantum number, n= 4, l= 1 ?)

A

s orbital

B

p orbital

C

dz2 orbital

D

dx2-y2 orbital

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.

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)

Which of the following spectral series in hydrogen atom gives spectral line of 4860 Å?

A

Lyman

B

Balmer

C

Paschen

D

Brackett

The NMR spectrum of ethanol (CH₃CH₂OH) comprises of three bunches of spectral lines. The number of spectral lines in the bunch corresponding to CH₂ group is

A

1

B

2

C

3

D

4

In the following sentence the word principal' occurs three times "The principal (1) aim of the principal (2) of the college was to help build new roads to link the area's principal (3)schools" Indicate the use(s) in which the meaning of the word “Principal is ‘chief or main',

A

Use (1)

B

Use(2)

C

Use (3)

D

Both (1) & (3)

An atom emits a photon of wavelength λ = 600 nm by transition from an excited state of life time 8 × 10^-9 s. If $$\Delta \nu $$ represents the minimum uncertainty in the frequency of the photon, the fractional width $$\frac{{\Delta \nu }}{\nu }$$ of the spectral line is of the order of

A

10-4

B

10-6

C

10-8

D

10-10

In a diatomic molecule, the inter-nuclear separation of the ground and first excited electronic state are the same as shown in the figure. If the molecule is initially in the lowest vibrational state of the ground state, then the absorption spectrum will appear as

A

B

C

D