Question
To decrease the cut-off wavelength of continuous X-rays by $$25\% ,$$ the potential difference across X-ray tube
A.
must be increased by $$\frac{{100}}{3}\% $$
B.
must be decreased by $$\frac{{100}}{3}\% $$
C.
must be increased by $$25\% $$
D.
must be decreased by $$25\% $$
Answer :
must be increased by $$\frac{{100}}{3}\% $$
Solution :
$$\eqalign{
& {\lambda _1} = \frac{{hc}}{{e{v_1}}};{\lambda _2} = \frac{{hc}}{{e{v_2}}} \cr
& \Rightarrow \frac{{{\lambda _2}}}{{{\lambda _1}}} = \frac{{{v_1}}}{{{v_2}}} \cr
& \Rightarrow \frac{3}{4} = \frac{{{v_1}}}{{{v_2}}} \cr
& \Rightarrow \left( {\frac{{{v_2} - {v_1}}}{{{v_1}}}} \right) \times 100 = \frac{{100}}{3} \cr} $$
Hence, $$P.D.$$ must be increased by $$\frac{{100}}{3}\% .$$