Hard `X` -rays for the study of fractures in bones should have a minimum wavelength of `10^(-11) m`. The accelerating voltage for electrons in `X` -ray machine should be

Options

A. `gt 124 kV`
B. `lt 124 kV`
C. between `60 kV` and `70 kV`
D. ` = 100 kV`

Answer

B

Explanation

From conservation of energy the elctron kinetic energy equals the maximum photon energy (we neglect the work function `phi` because it is normally so small compared to `eV_(0)`).
`eV_(0) = hv_(max)`
or `eV_(0) = (hc)/(lambda_(min))`
`:. V_(0) = (hc)/(e lambda_(min))`
or `V_(0) = (12400 xx 10^(-10))/(10^(-11)) = 124 kV`
Hence, accelerating voltage for electrons in `X` - ray machine should be less than `124 kv`.