Home | | Physics 12th Std | Wave nature of particles: Example Solved Numerical Problems

# Wave nature of particles: Example Solved Numerical Problems

Example Numerical Question with Answers, Solution - Wave nature of particles

Wave nature of particles

### EXAMPLE 7.6

Calculate the momentum and the de Broglie wavelength in the following cases:

i) an electron with kinetic energy 2 eV.

ii) a bullet of 50 g fired from rifle with a speed of 200 m/s

iii) a 4000 kg car moving along the highways at 50 m/s

Hence show that the wave nature of matter is important at the atomic level but is not really relevant at macroscopic level.

### Solution: From these calculations, we notice that electron has significant value of de Broglie wavelength (Ōēł10ŌĆō9m which can be measured from difraction studies) but bullet and car have negligibly small de Broglie wavelengths associated with them (Ōēł10ŌĆō33m and 10ŌĆō39m respectively, which are not measurable by any experiment). This implies that the wave nature of matter is important at the atomic level but it is not really relevant at the macroscopic level.

### EXAMPLE 7.7

Find the de Broglie wavelength associated with an alpha particle which is accelerated through a potential difference of 400 V. Given that the mass of the proton is 1.67 ├Ś 10ŌĆō27 kg.

### Solution

An alpha particle contains 2 protons and 2 neutrons. Therefore, the mass M of the alpha particle is 4 times that of a proton (mp) (or a neutron) and its charge q is twice that of a proton (+e).

The de Broglie wavelength associated with it is EXAMPLE 7.8

A proton and an electron have same de Broglie wavelength. Which of them moves faster and which possesses more kinetic energy?

### Solution

We know that ╬╗ = h/ ŌłÜ(2mK)

Since proton and electron have same de Broglie wavelength, we get Since me < mp , Kp < Ke , the electron has more kinetic energy than the proton. Since me < mp , Žģp < Žģe , the electron moves faster than the proton.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
12th Physics : UNIT 8 : Dual Nature of Radiation and Matter : Wave nature of particles: Example Solved Numerical Problems |