A `pi-meason` hydrogen atom is a bound state of negative charged pion (denoted by `pi^(bar), m_(pi) = 273 m_(e))` and a proton. Estimate the number of revolutions a `pi-meason` makes (averagely ) in the ground state on the atom before , it decays (mean life of a `pi-meason ~= 10^(-8) s`, mass of proton `= 1.67 xx 10^(-27) kg)`.

Options

A. `2xx10^(7)`
B. `2xx10^(10)`
C. `2xx10^(14)`
D. None

Answer

B

Explanation

`becauserprop(1)/(m)therefore(r_(pi^(-)))/(r_(e))=(m_(e))/(m_(pi^(-)))`
`r_(pi^(-))=(r_(e)m_(e))/(m_(pi^(-)))=1.94xx10^(-13)m`
`becauseV=(e^(2))/(2epsi_(0)h)=2.2xx10^(6)m//s`
`thereforeT_(pi^(-))=(2pir_(pi^(-)))/(V)=5.6xx10^(-19)sec`
`thereforen=(10^(-8))/(T_(pi^(-)))~=2xx10^(10)`