Physics Help?

Question

The relationship E= (1.24 *10 ^3) / λ, where E is the energy of a photon in electron colds and λ is the wavelength in nanometres, is a handy form of the equation E = (h*c) / λ. Substitute E=(h*c) / λ and make any necessary unit conversions, to show that E= (1.24*10^3) / λ, is valid for nanometres and electron volts.

Basically, i have to solve for h*c.. i did that and i got:

hc= (6.63 * 10 ^-34 J/s) * (3.0 * 10^8 m/s)
= 1.989 * 10 ^ -25 J/m

I now need to convert that into nanometres and electron volts (eV).
1 nm = 1.0 * 10^9 m and 1eV = 1.60 * 10^ -19 J

I'm having difficulty...anyone know how to solve this?

Answer 1

E = ( h c ) / λ
E = ( 6.63 x 10^-34 J-s ) ( 3.0 x 10^8 m / s ) / λ
E = ( 1.989 x 10^-25 J - m ) / λ

You got this far. Now convert J to eV...

E = ( 1.989 x 10^-25 J-m ) ( 1 ev / 1.602 x 10-19 J ) / λ
E = ( 1.24 x 10^-6 ev-m ) / λ

...and convert meters to nanometers...

E = ( 1.24 x 10^-6 ev-m ) ( 10^-9 nm / m ) / λ
E = ( 1.24 x 10^3 ev-nm ) / λ

...to arrive at the desired expression.