Answer:
Frequency = 3.16 ×10¹⁴ Hz
λ = 0.95×10² nm
Explanation:
Energy associated with nth state is,
En = -13.6/n²
For n = 1
E₁ = -13.6 / 1²
E₁ = -13.6/1
E₁ = -13.6 ev
Kinetic energy of electron = -E₁ = 13.6 ev
For n = 5
E₅ = -13.6 / 5²
E₅ = -13.6/25
E₅ = -0.544 ev
Kinetic energy of electron = -E₅ = 0.544 ev
Wavelength of radiation emitted:
E = hc/λ = E₅ - E₁
hc/λ = E₅ - E₁
by putting values,
6.63×10⁻³⁴Js × 3×10⁸m/s / λ = -0.544ev - (-13.6 ev )
6.63×10⁻³⁴ Js× 3×10⁸m/s / λ = 13.056 ev
λ = 6.63×10⁻³⁴ Js× 3×10⁸m/s /13.056 ev
λ = 6.63×10⁻³⁴ Js× 3×10⁸m/s /13.056 × 1.6×10⁻¹⁹ J
λ = 19.89 ×10⁻²⁶ Jm / 13.056 × 1.6×10⁻¹⁹ J
λ = 19.89 ×10⁻²⁶ Jm / 20.9 ×10⁻¹⁹ J
λ = 0.95×10⁻⁷ m
m to nm:
0.95×10⁻⁷ m ×10⁹nm/1 m
0.95×10² nm
Frequency:
Frequency = speed of electron / wavelength
by putting values,
Frequency = 3×10⁸m/s /0.95×10⁻⁷ m
Frequency = 3.16 ×10¹⁴ s⁻¹
s⁻¹ = Hz
Frequency = 3.16 ×10¹⁴ Hz
