Question

The uncertainty in time of an electron in 5th excited state in case of hydrogen atom
a)10^-5 s
b)10^-9 s
c)10^-8 s
d)10^-3 s

Solve please

Answer 1

we have to find the uncertainty in time of an electron in 5th excited state in case of hydrogen atom.

solution : first we have to find energy in 5th excited state.

here n = 6

using Bohr's energy formula, E = 13.6 × Z²/n² eV

= 13.6 × 1/6²

= 13.6/36

= 0.378 eV

= 0.378 × 1.6 × 10^-19 J

= 6.048 × 10¯²⁰ J

now applying Heisenberg's uncertainty principle,

∆E . ∆t = h/4π

⇒(6.048 × 10¯²⁰) × ∆t = (6.63 × 10¯³⁴)/(4 × 3.14)

⇒∆t = (6.63 × 10¯¹⁴)/(6 × 4 × 3.14)

⇒∆t = 0.087 × 10¯¹⁴ = 8.7 × 10¯¹⁶ ≈ 10¯¹⁵ sec

Therefore the uncertainty in time of an electron in 5th excited state in case of hydrogen atom is 10¯¹⁵ sec