Question

Assuming that having a velocity greater than velocity of light is not possible, find out the value of the highest atomic number of hydrogen like ion which can exist.
Given that the velocity of electron in the first orbit of Bohr hydrogen atom is $2.18\times {10}^6{\text{ms}}^{-1}$.

• A. $138$
• B. $238$
• C. $157$
• D. $257$

Answer 1

The correct option is A $138$

As per question, the maximum velocity will be 'c'.
Since the question has asked about highest atomic number which can exist, as per Bohr's theory, ${\text{v}}_n=2.18\times {10}^6\left(\frac{Z}{n}\right)$
Data of first orbit of hydrogen is given. Hence, expression becomes: ${\text{v}}_n=(2.18\times {10}^6)Z$
here $v_n=c=3\times {10}^8\text{m/s}$
Hence,
$3\times {10}^8=(2.18\times {10}^6)Z$
$\Rightarrow Z=\frac{3\times {10}^8}{2.18\times {10}^6}$
$\Rightarrow Z\approx 138$