An electron is allowed to move freely in a closed cubic box of length of side 10 cm. The uncertainty in its velocity will be :

Options

A. `3.35 xx 10^(-4) m sec^(-1)`
B. `5.8 xx 10^(-4) m sec^(-1)`
C. `4 xx 10^(-5) m sec^(-1)`
D. `4 xx 10^(-6) m sec^(-1)`

Answer

A

Explanation

If a is side of cube, the `a sqrt(3)`
`therefore Delta x = 10 sqrt(3) cm = 10 sqrt(3) xx 10^(-2) m`
`Delta x . Deltap = (h)/(4pi) , Delta x .m,Deltav = (h)/(4pi)`
`Delta v = (h)/(4 pim.Deltax)`
`= (6.63 xx 10^(-34))/(4xx3.14 xx 9.1xx10^(-31)xx sqrt(3) xx 10^(-2))`
` = therefore Deltav ~= 3.35 xx 10^(-4) ms^(-1)`