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Q.
Which of the following have highest specific charge?
BHUBHU 2005Dual Nature of Radiation and Matter
Solution:
Specific charge is equal to ratio of charge to mass. If charge is q and mass m then the ratio of charge (q) to mass (m) is known as specific charge. For positron,
$ {{m}_{e}}=9.1\times {{10}^{-31}}kg,e=1.6\times {{10}^{-19}}C $
$ \frac{e}{m}=\frac{1.6\times {{10}^{-19}}}{9.1\times {{10}^{-31}}} $
$ =1.75\times {{10}^{11}}Ck{{g}^{-1}} $
For proton, $ {{m}_{p}}=1.67\times {{10}^{-27}}kg,e=1.6\times {{10}^{-19}}C $ $ \frac{e}{m}=\frac{1.6\times {{10}^{-19}}}{1.67\times {{10}^{-27}}} $
$ =9.58\times {{10}^{7}}Ck{{g}^{-1}} $
For helium, $ {{m}_{He}}=6.6\times {{10}^{-27}}kg,{{q}_{He}}=2\times 1.6\times {{10}^{-19}}C $
$ \frac{e}{m}=\frac{2\times 1.6\times {{10}^{-19}}}{6.6\times {{10}^{-27}}}=4.84\times {{10}^{7}}Ck{{g}^{-1}} $
Hence, positron has highest specific charge.