Optionals IAS Mains Physics: Questions 93 - 99 of 306

Applying integration by parts on the above integral

It is clear that exponential will “beat” any power function as of tends to.

Hence N is proportional to.

• Planck’s formula is given by
• Differentiating it partially with respect to, we get
• For maximum value of emission, i. e. for maximum value of must be equal to zero i.e..
• Putting, the above expression becomes
• It is obvious from this equation that there must be a root in the neighbourhood of 5. Applying the method of approximation the exact value

Formula used:

Here we have applied formula of integration by parts

I. e.

Denominator: (calculated previously)

Numerator:

Divided and multiplied by 2 and

If the particle is acted upon by the forces which are conservation, that is, if the forces are derivable form a scalar potential energy function in the manner then the total energy of the particle (Kinetic + Potential) is conserved.

Suppose, under the action of such a force, a particle moves form particle will be

If the particle moves distance in

A simple relation between relativistic momentum (and relativistic energy (E) of a particle of rest mass is easily obtained from the expressions for and . For, clearly , so that

Which enables us to determine the velocity of the particle from the values of its momentum and energy since, clearly,

Another important relation between and E may be obt