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Question

Find the
(a) maximum frequency
(b) Minimum wavelength of X-rays produced by 30 kV electrons.


Solution

(a). Potential of the electrons, $$V = 30 kV = 3 × 10^4 V$$
Hence, energy of the electrons, $$E = 3 × 104 eV$$
Where,
e = Charge on an electron = $$1.6 × 10^{−19} C$$
Maximum frequency produced by the X-rays is $$\nu$$
The energy of the electrons is given by the relation is $$E=h\nu$$
Where,
h = Planck’s constant = $$6.626 × 10^{−34}Js$$ 
$$\nu=E/h=7.24\times 10^{18}Hz$$

(b). Energy of a electron, $$E=30\times 10^3eV$$
Let Maximum frequency produced by the X-rays be $$\nu$$
$$\nu=E/h=1.6\times 10^{-19}\times 3\times 10^4/6.626\times 10^{-34}=7.24\times 10^{18}Hz$$ where $$h$$ is the planck's constant.
The minimum wavelength produced by the X-rays is given as-
$$\lambda=c/\nu=0.0414nm$$

Physics
NCERT
Standard XII

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