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



Data Given:

`\E_i` = -3.5 ｘ 10⁻¹⁹ J 

`\E_f` = -1.2 ｘ10⁻¹⁸ J = -12 ï½˜ 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 = Î» =  ?



Solution:

Since we have

λ = `\frac {hc}{E_i - E_f}`

λ = `\frac {6.62 ｘ 10⁻³⁴ m² kg s⁻¹ ｘ 3 ｘ 10⁸ m s⁻¹}{-3.5 ｘ 10⁻¹⁹ J - (-1.2 ｘ10⁻¹⁸ J)}`


λ = `\frac {19.86 ｘ 10⁻²⁶ m³ kg s⁻²}{-3.5 ｘ 10⁻¹⁹ J + 12 ｘ 10⁻¹⁹ J}`

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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