Question

What is the energy in joules required to shift the electron of the hydrogen atom of the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emmitted when the electron returns to ground state ? the ground state electron energy is -2 .18*10 -11​

Answer 1

Answer:

E₁ = - 2.18 × 10⁻¹¹ ergs

En = E₁ / n²

E₅ = (-2.18 × 10⁻¹¹) / 5²

E₅ = (-2.18 × 10⁻¹¹) / 25 = - 8.72 × 10⁻¹³

ΔE = E₅ - E₁

= - 8.72 × 10⁻¹³ - (- 2.18 × 10⁻¹¹) = 2.09828 × 10⁻¹¹ ergs.

1 ergs = 10⁻⁷ joules

Converting in joules :

2.09828 × 10⁻¹¹ × 10⁻⁷ = 2.09828 × 10⁻¹⁸ Joules

ΔE = hc/y

Y = wavelength

h = planks constant = 6.62 × 10⁻³⁴

c = speed of light = 3.0 × 10⁸

Doing the substitution we have :

2.09828 × 10⁻¹¹ = (6.62 × 10⁻³⁴ × 3 × 10⁸) / Y

Y = (6.62 × 10⁻³⁴ × 3 × 10⁸) / (2.09828 × 10⁻¹¹) = 9.465 × 10⁻¹⁵ cm

= 9.465 × 10⁻¹⁵ cm

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