# Class 12 Physics Dual Nature Of Radiation And Matter: NCERT Solutions for Question 1

This page focuses on the detailed Dual Nature Of Radiation And Matter question answers for Class 12 Physics Dual Nature Of Radiation And Matter, addressing the question: 'Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 1

## Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.

Potential of the electrons, V = 30 kV = 3 × 104 V

Hence, energy of the electrons, E = 3 × 104 eV

Where,

e = Charge on an electron = 1.6 × 10−19 C

(a)Maximum frequency produced by the X-rays = ν

The energy of the electrons is given by the relation:

E =

Where,

h = Planck’s constant = 6.626 × 10−34 Js

So  v = E / h

= 1.6 x 10-19 x 3 x 104 / 6.626 x 10-34 = 7.24 x 1018 Hz

Hence, the maximum frequency of X-rays produced is 7.24 x 1018 Hz

(b)The minimum wavelength produced by the X-rays is given as:

λ = c / v

= 3 x 108 / 7.24 x 1018 = 4.14 x 10-11 m = 0.0414 nm

Hence, the minimum wavelength of X-rays produced is 0.0414 nm.