Calaculate the wavelength of the particle in the following tow cases: `(i)` The fastest serve in tennis is about `130` miles per hour, or `58ms^(-1)`. Calculate the wavelength associated with a `6.0xx10^(-2) kg` tennis bell travelling at this speed. `(ii)` Calculate the wavelength associated with an electorn moving at `58ms^(-1)`.
Strategy : The de Broglie relationship says that the wavelength `lambda` of an object with mass `m `moving at a velocity `v` can be calculated by the equation `lambda = h//mv`.

Explanation

`(i) lambda = (h)/(mv)`
`((6.63xx10^(-34)kgm^(2)s^(-1)))/((6.0xx10^(-2)kg)(58ms^(-1)))`
`=0.019 xx 10^(-32)m`
`= 1.9xx10^(-34)m`
Note that Planck's constant, which is usually expressed in units of juole seconds `(J s)`, is expressed for the present purposes in units `kg m^(2)s^(-1)` because teh conversion factor is `1J = 1kg m^(2) s^(-2)`.
`(ii) lambda = (h)/(mv)`
`((6.63xx10^(-34)kgm^(2)s^(-1)))/((9.1xx10^(-31)kg)(58ms^(-1)))`
`= 0.013 xx 10^(3)m`
`= 1.3 xx 10^(-5)m`
` (1.3xx10^(-5)m) ((10^(9)nm)/(1m))`
`= 1.3xx10^(4)nm`