The work function ( (W₀ ) ) of ( Li , K , Mg , Ag ) and ( Cu ) are (2.42,2.25,3.70,4.30 ) and (4.80 eV ) respectively. The number of metals which undergo photoelectric effect if a radiation of wavelength (540 ~nm ) falls on them is ( (1 eV =1.602 10⁻¹⁹ ~J ) )

Step-by-step solution

Key Idea For any metal to show photoelectric effect, (v > v₀ ), where (v₀ ) is threshold frequency, (v ) is the frequency of light. Given, ( aligned W₀ of Li =2.42 eV & =2.42 1.602 10⁻¹⁹ ~J & =3.876 10⁻¹⁹ ~J aligned ) (W₀ ) of ( K =2.25 eV =3.604 10⁻¹⁹ ~J ) (W₀ ) of ( Mg =3.70 eV =5.927 10⁻¹⁹ ~J ) (W₀ ) of ( Ag =4.30 eV =6.888 10⁻¹⁹ ~J ) (W₀ ) of ( Cu =4.80 eV =7.689 10⁻¹⁹ ~J ) Also ( W₀=h v₀ ) ( v₀ ) of ( Li =W₀ / h ) (= 3.876 10⁻¹⁹ 6.626 10⁻³⁴ =0.584 10¹⁵ ~s ⁻¹ ) ( v ₀ ) of ( K = W₀ h = 3.604 10⁻¹⁹ 6.626 10⁻³⁴ )