If the kinetic energy of a particle is increased by 10 times, the percentage change in the de Broglie wavelength of the particle is

Options

A. `25 %`
B. `75%`
C. `60%`
D. `50%`

Answer

B

Explanation

de Broglie wavelength `lamda=(h)/(sqrt(2mk))` where m is the mass and K is the kinetic energy of a particle .
Since m remains the same
`:. lamda prop 1/sqrtK:. (lamda.)/lamda=sqrt(K/(K.))=sqrt(1/16)=1/4 `
% change in wavelength `=((lamda - lamda.)/(lamda)) xx 100`
`= (1-(lamda.)/(lamda))xx100 = (1-(1)/4) xx100 = 75%`