Postulates Of Quantum Mechanics NAT - IIT JAM MCQ

Applying time independent Schrödinger equation

Substituting (2) in (1)

Putting V(x = 0) = 0  in (3)

The correct answer is: 0.5

Energy emitted due to transition of electron -

Wherin

Longest wavelength in balmer series is corresponding to transition between 

Lets say it is 

Longest wavelength in lymen series is corresponding to transition between  2 ---> 1

Lets say it is 

=0.1852

Solution= 

eV_s1=hv- Φ₁

eV_s2=hv- Φ₂

eV_s1= eV_s2

eV_s1/eV_s2 = hv- Φ₂/ hv- Φ₁=1/2

2hv-2Φ₂ = 1hv- Φ₁

2Φ₂ = hv+ Φ₁

2Φ₂ = 5+1.5

2Φ₂ = 6.5eV

Φ₂ = 3.25eV

The correct answer would be 3.25eV

Now A² = 2/L = from normalization of ψ
∴    Probability = 1/3 = 0.33
The correct answer is: 0.33

The number of nodes in a wavefunction determine the energy level. In this case there is just one node. Thus, this is E₂. The lowest would be E₁.
E_n = (const)n²
Since E₂ = 2 = (constant) 4

The correct answer is: 0.5

The correct answer is: 0.18

We know,

With  E = 5eV  and  V₀ = 16eV

With  a = 0.5 × 10^–9 m,  m = 9.1 × 10^–31 kg,  V₀ = 6eV,  E = 5V   and 

Hence the percentage of probability of tunneling is 1.33.
The correct answer is: 1.33

The eigenvalue of energy

when the particle is in the least energy state (n = 1), the energy
with h = 6.62 × 10^–34 Js, m = 9.1 × 10^–31 kg and a = 1 × 10^–10 m

After calculating,

The correct answer is: 37.62 eV

For a hydrogen atom,

Now, for most probable r. We need to minimize the probability w.r.t. r.

Putting (2) in (1)

The correct answer is: 1