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Use the Same Formula You Employ in (A) to Obtain Electron Speed for an Collector Potential of 10 Mv. Do You See What is Wrong? in What Way is the Formula to Be Modified? - CBSE (Science) Class 12 - Physics

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Question

Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?

Solution

Potential of the anode, V = 10 MV = 10 × 106 V

The speed of each electron is given as:

`v = (2V e/m)^(1/2)`

`= (2xx10^7 xx 1.76 xx 10^11)^(1/2)`

`= 1.88 xx 10^9 "m/s"`

This result is wrong because nothing can move faster than light. In the above formula, the expression (mv2/2) for energy can only be used in the non-relativistic limit, i.e., forv << c.

For very high speed problems, relativistic equations must be considered for solving them. In the relativistic limit, the total energy is given as:

E = mc2

Where,

= Relativistic mass

`= m_0 (1 - v^2/c^2)^(1/2)`

m0 = Mass of the particle at rest

Kinetic energy is given as:

K = mc2 − m0c2

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 11: Dual Nature of Radiation and Matter
Q: 20.2 | Page no. 409
Solution Use the Same Formula You Employ in (A) to Obtain Electron Speed for an Collector Potential of 10 Mv. Do You See What is Wrong? in What Way is the Formula to Be Modified? Concept: Experimental Study of Photoelectric Effect.
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