Saved Bookmarks
| 1. |
Obtain the first Bohr's radiusand the groundstate energy of muonichydrogen atom [i.e., an atom in whicha negatively charged (mu^(-)) of mass about 207 m_(e) orbits around a proton]. |
|
Answer» Solution :According to Bohr.s theory of hydrogen atom radius of nth orbitwill be `r_(N) = (in_(0) n^(2) h^(2))/(pi me^(2))rArr r_(n) oo (1)/(m)` `therefore ` Radius of first Bohr.s orbit for a muonic hydrogen atom . `r_(m) = (r_(e).m_(e))/(m_(m)) = (5.3 xx 10^(-11).m_(e))/(207 m_(e)) =2.56 xx 10^(-13) m` Similarly EXPRESSION for energy `E_(n) = - ( me^(4))/(8 in_(0)^(2) n^(2) h^(2))`suggests that `E_(n) prop m` `therefore ` Energyin 1 st orbit of muonichydrogen atom will be `E_(m) = (E_(e) .m_(m))/(m_(e)) =((-13.6 eV).207 m_(e))/(m_(e)) = - 2.8 xx 10^(3) eV = - 2.8 KeV` |
|