Question

Electrons of 1.68x 105 j/mol kinetic energy are emitted when electromagnetic radiations of 300nm wavelength fall on Na metal. What is the maximum wavelength of light to exhibit photoelectric effect?​

Answer 1

Given:

Electrons of 1.68x 105 j/mol kinetic energy are emitted when electromagnetic radiations of 300nm wavelength fall on Na metal.

To find:

What is the maximum wavelength of light to exhibit photoelectric effect?​

Solution:

From given, we have,

Electrons of 1.68x 105 j/mol kinetic energy are emitted when electromagnetic radiations of 300nm wavelength fall on Na metal.

The wavelength = 300nm = 300 ×  10⁻⁹m

we use the formula

E = hv = hc/λ

⇒(6.62 × 10⁻³⁴ × 3 × 10⁸)/300 × 10⁻⁹

=6.62 × 10⁻⁹J

so, Kinetic energy for 1 mole of photons = 6.62 × 10⁻⁹ × 6.022 × 10²³

= 3.99 × 10⁵J

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

= (3.99 × 10 ⁵) - (1.68 × 10⁵)

= 2.31 × 10 ⁵J

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

⇒ 2.31 × 10⁵/6.022 × 10²³  = 3.84 × 10⁻¹⁹ J

Now maximum wavelength,

λ = hc/E

= (6.62 × 10⁻³⁴ × 3 × 10⁸)/3.84 × 10 ⁻¹⁹

=5.17 × 10⁻⁷m = 517nm

Therefore, the maximum wavelength of light to exhibit photoelectric effect is 517nm