Question
An X-ray tube is operated at $$15\,kV.$$ Calculate the upper limit of the speed of the electrons striking the target.
A.
$$7.26 \times {10^7}\,m/s$$
B.
$$7.62 \times {10^7}\,m/s$$
C.
$$7.62 \times {10^7}\,cm/s$$
D.
$$7.26 \times {10^9}\,m/s$$
Answer :
$$7.26 \times {10^7}\,m/s$$
Solution :
The maximum kinetic energy of an electron accelerated through a potential difference of $$V$$ volt is $$\frac{1}{2}m{v^2} = eV$$
∴ maximum velocity $$v = \sqrt {\frac{{2eV}}{m}} $$
$$\eqalign{
& v = \sqrt {\frac{{2 \times 1.6 \times {{10}^{ - 19}} \times 15000}}{{9.1 \times {{10}^{ - 31}}}}} , \cr
& v = 7.26 \times {10^7}\,m/s \cr} $$