Question

When electromagnetic radiation of wavelength 300nm falls on the surface of sodium, electrons are emitted with a kinetic energy of 1.68 x 10 5 . What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted?

Answer 1

The minimum energy needed is 2.31×10⁵J⋅mol-1 and the maximum wavelength is 518 nm.
E = hv = hc/v
Putting the values we get,
E = 6.62 X 10⁻¹⁹ J
So, the enery for one mole of photons = 6.62 x 10⁻¹⁹ x6.62 X 10⁻¹⁹ = 3.99 x 10⁵J
So, minimum amount of energy required= 3.99×10⁵−1.68×10⁵= 2.31 x 10⁵ j

wavelength= Nhc/ Ф = 6.022 x 10²³ x 6.626 x 10⁻³⁴ x 2.998 x 10⁸/ 2.31 x 10⁵
=518mm

Answer 2

Explanation:

Given:

wavelength =300nm=300x 10⁻⁹m

h=planks constant=6.62 x 10⁻³⁴Js

c=velocity of light =3x10⁸ m/s

E=hv=hc/λ

⇒(6.62 x 10⁻³⁴ x3x10⁸)/300x 10⁻⁹

=6.62 x 10⁻⁹J

so, Kinetic energy for for 1 mole of photons=6.62 x 10⁻⁹ x6.022 x 10²³

=3.99x 10⁵J

so ,minimum amount of energy required to remove 1 mole of electrons from sodium atoms is

=(3.99 x 10 ⁵)- (1.68 x 10⁵)

=2.31 x 10 ⁵J

∴  minimum energy required to remove 1 electron from Na atom=

⇒2.31 x 10⁵/6.022 x 10²³

⇒3.84 x 10⁻¹⁹ J

Now maximum wavelelngth = λ=hc/E=(6.62 x 10⁻³⁴ x 3 x 10⁸)/3.84x 10 ⁻¹⁹

=5.17 x 10⁻⁷m=517nm