Question

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? What is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is -2.18 x 10^(-11) ergs.

Answer 1

(i) Energy = -Rh(1/n1²) - (1/n2²)

where,  

n1 = initial orbit

n2 = final orbit

Rh = Rydberg constant (2.18 X 10⁻¹⁸)

First energy level (n1) = 1

Second energy level (n2) = 5

Energy = 2.18 X 10⁻¹⁸((1/1²) - (1/5²)

= 2.18 x 10⁻¹⁸((1/1) - (1/25)

= 2.18 x 10⁻¹⁸ x ((25-1)/25)

= 2.18 x 10⁻¹⁸ x ((24)/25)

= 2.18 x 10⁻¹⁸ x 24/25

= 52.3 x 10​⁻¹⁸/25

​​= 2.09 x 10⁻¹⁸ J

∴ 2.09 x 10⁻¹⁸ J  of energy is required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit.

(ii) Wavelength (λ) = hc/E  

where,

h = Plank constant

c = speed of light

E = energy

​​Wavelength

= 6.626 x 10^(-34) x 3.0 x 10⁸/2.09 x 10⁻¹⁸

= 19.87 x 10^(-26)/2.09 x 10⁻¹⁸

= 9.50 x 10⁻⁸ m

∴ Wavelength of the light emitted when the electron returns to the ground state is 9.50 x 10⁻⁸ m.

Answer 2

Answer:

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