Origin Of Quantum Mechanics NAT Level – 2 - Physics MCQ

From the energy time uncertainty

The correct answer is: 1.59 x 10¹¹ Hz

The correct answer is: 1.206

The correct answer is: 7.085

de Broglie wavelength

Compton wavelength 


The correct answer is: 0.707

For symmetric scattering θ = φ
From the relation between  θ & φ


The correct answer is: 41.4

Average life time = Δt = uncertainty in time = 10^–8s


 

width of the line = 1.9 × 10^–14 m
The correct answer is: 19

K.E. of recoiled e^– is
E = 4 × 10³ × 1.6 × 10^–19 Joules = 6.4 × 10^–16 J

= 34.13 × 10^–24 kg m/s

From conservation of momentum

solving (i) & (ii)

The correct answer is: 0.35

Radius of nucleus = 10^–14 m
∴ Uncertainty in position 

= 1.054 × 10^–20 kg m/s
Mass of α particle = 4m_p = 4 × 1.67 × 10^–27 kg
0
The correct answer is: 52

Distance between two peaks = Δλ

The correct answer is: 90

For a helium atom

Because momentum of electron 1, 
and momentum of electron 2, 
p₁,  p₂ is the spread in momentum corresponding to electron 1 & 2 respectively.

r₁, r₂  is the localization of electron 1 & 2 respectively.

Total energy, E = K.E + Interaction energy of e₁ and e₂ + Interaction energy between nucleus and electrons

Interaction Energy between 
Since the separation between r₁ and r₂ is of the order r₁ + r₂ and k = 1 in natural system of units.
 Interaction between nucleus and electron

For the ground state energy
 since in the ground state, Energy is minimum.

solving these two equations, we get

substituting r₁ and r₂ in the expression for E

E_min = –10.34 eV
Put  m = 9.1 × 10^–31 kg
e = 1.6 × 10^–19C

The correct answer is: -10.34