Question

The radius of first Bohr orbit of hydrogen atom is $0.53\AA$ . Then the radius of first Bohr orbit of mesonic atom (negative meson has mass $207$ times that of electron but same charge) is:

• A. $2.85\times {10}^{-13}\text{m}$
• B. $1.06\times {10}^{-13}\text{m}$
• C. $0.53\times {10}^{-10}\text{m}$
• D. $7.0\times {10}^{-12}\text{m}$

Answer 1

The correct option is A $2.85\times {10}^{-13}\text{m}$

As radius of $n^{\text{th}}$ orbit is inversely proportional to the mass of electron, for mesonic atom we use reduced mass of electron as
$\mu =\frac{m_p\left(207m_e\right)}{m_p+207m_e}$
As $m_p=1840m_e$
$\Rightarrow \frac{1840\times 207}{1840+207}{m}_e$
$\Rightarrow \mu =186m_e$
Thus, radius of first orbit of mesonic atom is
$r=\frac{0.53\times {10}^{-10}}{186}=2.85\times {10}^{-13}\text{m}$