Question

Arsenic will emit light at a wavelength of 193.7 nm. Calculate the energy and frequency corresponding to this wavelength.

Answer 1

Wavelength of arsenic emission, λ = 197.3 nm

= (197.3 nm)*(1 m)/(1.0*10⁹ nm) [1 nm = 1.0*10^-9 m]

= 1.973*10^-7 m.

It is known that

ν*λ = c

where c = 2.998*10⁸ m.s^-1 is the speed of the emission through vacuum.

Plug in values and get

ν*(1.973*10^-7 m) = 2.998*10⁸ m.s^-1

=====> ν = (2.998*10⁸ m.s^-1)/(1.973*10^-7 m)

=====> ν = 1.5195*10¹⁵ s^-1 ≈ 1.519*10¹⁵ Hz

The frequency of the emission is 1.519*10¹⁵ Hz (ans).

The energy of the emission is given as

E = hν

where h = 6.626*10^-34 J.s is the energy of the emission.

Plug in values and get

E = (6.626*10^-34 J.s)*(1.519*10¹⁵ s^-1)

= 1.006*10^-18 J (ans).