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

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Solution

Here,
Voltage, V = 30 kV = 30 x 10³V = 3 x 10⁴V

(a) Using the formula,

{hv}_{\max} = eV

v_{\max} = \frac{eV}{h} = \frac{1.6 \times 10^{- 19} \times 3 \times 10^{4}}{6.63 \times 10^{- 34}} Hz

= 7.24 \times 10^{18} Hz

is the required maximum frequency.

(b) Minimum wavelength of x-rays produced,

λ_{m i n} = \frac{c}{v_{\max}} = \frac{3 \times 10^{8}}{7.24 \times 10^{18}} m

\Rightarrow

λ_{m i n} = 0.414 \times 10^{- 10} m = 0.414 Å

= 0.0414 nm .

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