Question

If an atom were to emit a photon whose wavelength was 5200 A, how much energy did the atom lose. answer 3.8 x 10^-19. I got 3.8/ 3.6 x 10^-20 is it wrong ????
How much energy would a mole of these atoms lose? 230 kJ answer. Please explain
and
Cesium metal requires 4.78 x 10^-19 J of energy to remove an electron from its surface. What is the longest wavelength of radiation sufficient to eject such a photoelectron? Why is this a maximum wavelength? answer should be 4.16 x 10^-7 explain how to get answer.

Answer 1

1)

Given that

wavelength λ = 5200 A^o = 5200 x 10^-10 m ( 1 A^o = 10^-10 m )

Energy E = hc / λ

h = planck's constant = 6.626 x 10^-34 J.s

c = velocity of light = 3 x 10⁸ m/s

Hence,

  E = hc / λ

=  (6.626 x 10^-34 J.s) (3 x 10 ⁸ m/s) / (5200 x 10^-10 m)

= 3.8 x 10^-19 J

E =   3.8 x 10^-19 J

2) 1 mole = 6.023 x 10²³

Energy lost by 1 mole of atoms =  6.023 x 10²³ x 3.8 x 10^-19 J = 230 kJ

3) Energy E = hc / λ

λ = hc/E

=  (6.626 x 10^-34 J.s) (3 x 10 ⁸ m/s) / ( 4.78 x 10^-19 J)

= 4.16 x 10^-7 m

λ = 4.16 x 10^-7 m