Examples

Example 5.1 Find the wavelength of the photon emitted in the transition of a hydrogen atom from n2 = 110 to ni = 109.

1092 1102

whence

This is in the radio band. Such radiation was observed for the first time in 1965 by an NRAO radio telescope.

Example 5.2 The effective temperature of a star is 12,000 K and the absolute bolometric magnitude 0.0. Find the radius of the star, when the effective temperature of the Sun is 5000 K and the absolute bolometric magnitude 4.7.

Thus the radius is twice the Solar radius.

Example 5.3 Derive the Wien displacement laws.

Let us denote x = hc/(kkT). Planck's law then becomes

2k5 T

For a given temperature, the first factor is constant. Thus, it is sufficient to find the maximum of the function f(x) = x5/(ex — 1).

First we must evaluate the derivative of f:

Telescopes Mastery

Telescopes Mastery

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