Question

Question 2.18 What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.

Class XI Structure of Atom Page 66

Answer 1

here we have to use formula ,
∆E = E₅ - E₁
where E₅ denotes energy in 5th orbit.
E₁ denotes energy in 1st orbit.

∆E = E₅ - E₁ = 2.18 × 10^-11 [ 1/n₁² - 1/n₅² ] erg
[ because we know,
Ef - Ei = 2.18 × 10^-11 ( 1/ni² - 1/nf²) erg ]

∆E = 2.18 × 10^-11 [ 1/1² - 1/5² ] erg
= 2.18 × 10^-11 [ 1 - 1/25 ] erg
= 2.18 × 10^-11 × 24/25 erg
= 2.0928 × 10^-11 erg or, 2.0928 × 10^-18 J

now,
∆E = hc/λ
λ = hc/∆E
= 6.626 × 10^-34 Js × 3 × 10^8 m/s/2.0928 × 10^-18 J
= 9.498 × 10^-8 m
= 949.8 × 10^-10 m
= 949.8 A°

hence, wavelength = 949.8 A°