An electron jumps from a level Ei = -3.5 ｘ 10⁻¹⁹ J to Ef = -1.2 ｘ10⁻¹⁸ J. What is the wavelength of the emitted light? (Ans: 234 nm)



Data Given:

Ei = -3.5 ｘ 10⁻¹⁹ J 

Ef = -1.2 ｘ10⁻¹⁸ J = -12 ｘ 10⁻¹⁹ J

∴ Plank's Constant = h =  6.62 ｘ 10⁻³⁴ m² kg s⁻¹

∴ Speed of light = 3 ｘ 10⁸ m s⁻¹


To Find:

The wavelength of the electron = λ =  ?



Solution:

Since we have

λ = hcEi-Ef

λ = 6.62ｘ10⁻³⁴m²kgs⁻¹ｘ3ｘ10⁸ms⁻¹-3.5ｘ10⁻¹⁹J-(-1.2ｘ10⁻¹⁸J)


λ = 19.86ｘ10⁻²⁶m³kgs⁻²-3.5ｘ10⁻¹⁹J+12ｘ10⁻¹⁹J

λ = 2.336 ｘ 10⁻⁷ m 

or

λ = 233.6 ｘ 10⁻⁹ m 

or

λ = 233.6 nm ------------------Ans.






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