Question

The energy of a photon is 2 eV. Find its frequency and wavelength.  

Answer 1

Given:

E = 2 eV = 2 × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻¹⁹ J 

To find:

1. Frequency (ν)
2. Wavelength (λ) 

Formulae:

1. E = hν
2. λ = `c/ν`  

Calculation:

i. Using formula (i),

v = `(3.2 xx 10^-19)/(6.63 xx 10^-34)`

= `(3.2 xx 10^15)/6.63`

= antilog {log (3.2) + log(10¹⁵) − log(6.63)}

= antilog {0.5051 + 15 − 0.8215}

= antilog {14.6836}

= 4.826 × 10¹⁴ Hz 

The frequency of photons is 4.826 × 10¹⁴ Hz.

ii. Using formula (ii),

`λ = c/ν = (3 xx 10^8)/(4.826 xx 10^14)`

= antilog {log 3 − log 4.826} × 10⁻⁶ 

= antilog {0.4771 − 0.6836} × 10⁻⁶ 

= antilog {`overline1`.7935} × 10⁻⁶  

= 0.6216 × 10⁻⁶m

= 6216 × 10⁻⁵ m

= 6216 Å   

The wavelength of the photon is 6216 Å.