Important Questions on the Dual Nature of Radiation and Matter

Initially, radiation was believed to have a wave nature. It was proven by Maxwell’s equations and experiments conducted by Hertz. Around the same time, several different experiments hinted toward the possibility of light having a particle nature. William Crookes is credited with the discovery of cathode rays in 1870, which was a huge milestone in establishing the particle nature of radiation. Radiation, thus, has a dual nature – both particle and wave. There are usually several questions asked in exams on this topic. Read on to find out more about the dual nature of radiation and matter.

Important questions

1. There is a photon of wavelength 600 nm. What is the energy and frequency of this photon?
   Ans: The energy of a photon can be related with its frequency as E = h𝜈, where E is the energy of the photon, h is the Planck’s constant whose value is 6.6 x 10-34 J sec, and 𝜈 is the frequency.

    

Also, 𝜈 = c/𝜆; where c is the speed of light and 𝜆 its wavelength.

𝜆 = 600 nm = 6 x 10-7 m

Hence, E = 6.6 x 10-34 x 3 x 108 / 6 x 10-7 = 3.3 x 10-19 J or 3.3 eV

Frequency, 𝜈 = 3 x 108 / 6 x 10-7 = 5 x 1014 sec-1 

1. Define the phenomenon of photoelectric emission.
   Ans: When radiation is made incident on the surface of a metal, the surface electrons absorb the radiation’s energy to overcome the electrostatic force of attraction by the positive ions on the surface. The electrons are ejected from the surface, and they escape into the surrounding atmosphere. This phenomenon is known as the photoelectric emission, and it was discovered by Hertz.
   A basic requirement for this is that the energy of the incident radiation should be equal to or greater than the energy of the electron.

    

2. Two metals X and Y have a work function of 15 eV and 20 eV respectively. For which metal would the threshold wavelength be higher?
   Ans: There is an inverse proportionality relation between threshold wavelength and work function. The higher the work function, the lower would be the threshold wavelength. Hence, the threshold wavelength would be higher for Y.

    

3. Find the value of the stopping potential of an electron whose maximum kinetic energy is 5eV.
   Ans: Stopping potential is defined as the retarding potential, which is given to the metal such that the flow of photoelectrons stops. The value of stopping potential is equal to the value of maximum kinetic energy, which in this case is 5eV.
    
4. Two materials X and Y of different work functions (such that the work function of X is smaller than that of Y) were radiated with X-rays. In which case would the kinetic energy be higher?
   Ans: If the radiation of the same energy is incident on both the materials, then the kinetic energy of those emitted electrons would be higher whose work function had a lower value. Hence, the kinetic energy would be higher in the case of electrons emitted from the surface of X.

    

5. Find the kinetic energy of the fastest-moving electron and the slowest-moving electron when radiation of wavelength 200 nm is made incident on a metal surface whose work function is 4.2 eV.
   Ans: Kinetic energy of the fastest moving electron = energy of radiation – work function
   Hence, K.Emax = hc/𝜆  – 𝛟

    

K.Emax = (6.6 x 10-34 x 3 x 108)/ (2 x 10-7) – (4.2 x 10-19)

= 2 x 10-19 J or 2 eV

The kinetic energy of the slowest-moving electron would be zero, as the velocity of such an electron would be zero.

1. Find the momentum, speed, and wavelength of an electron having the kinetic energy of 100eV.
   Ans: K.E = 0.5 x mv2

    

100 x 10-19 = 0.5 x 9.1 x 10-31 x v2

Solving this, v = 5.9 x 106 m/s

Wavelength, 𝜆 = h/mv

𝜆 = 6.6 x 10-34/ (9.1 x 10-31 x 5.9 x 106)

𝜆 = 123 pm (pm being picometer)

Momentum, p = mv

p= 9.1 x 10-31 x 5.9 x 106 = 5.4 x 10-24 kg m/s

1. The energy of incident radiation is greater than the threshold frequency of the material upon which the radiation is incident. What would be the effect on the kinetic energy of ejected electrons and on photoelectric current if the frequency of incident radiation is doubled?
   Ans: Kinetic energy increases when the frequency of the incident radiation increases. Photoelectric current, however, remains – the number of electrons that would be ejected would remain the same (only their speed will change).

    

2. Why is the wavelength of a large particle like a tennis ball not visible?
   Ans: The wavelength of a particle is inversely proportional to its size, as 𝜆 = h/mv (De-Broglie’s equation). So, the larger the size, the smaller the wavelength. A tennis ball would be so big that the wavelength associated with it would be invisible to the human eye.

    

3. Find the ratio of de-Broglie wavelength for an α-particle and a proton, having the same potential difference.
   Ans: Momentum of a particle, p = (2mqV)1/2

    

The mass of an α-particle is four times that of a proton. The charge on an α-particle is twice that on a proton.

Hence, pα-particle/pproton = 22/1

𝜆 is inversely proportional to momentum, so 𝜆α-particle/𝜆proton = 1/ 22

Conclusion

Once you have understood the dual nature of radiation and matter concept, doing dual nature of radiation and matter – important questions is the next step. Questions of this topic are frequently asked in the examination, and hence their wholesome understanding is crucial. This article covered the frequently asked questions on this topic, that would be enough for your exams.