What is the velocity of a 0.400 - kg billiard ball if its wavelength is 7.50 cm (large enough for it to interfere with other billiard balls)?

Consider the expression for the De Broglie's formula.

\[{\bf{v = }}\frac{{\bf{h}}}{{{{\bf{m}}_{{\bf{proton }}}}{\bf{\lambda }}}}\]

Here, h is the planks constant, with a value of \[6.62 \times {10^{ - 34}}{\rm{\;kg}} \cdot {{\rm{m}}^{\rm{2}}} \cdot {\rm{s}}\]

Considering the given information:

Wavelength is\[\lambda = {\rm{6}}{\rm{.00}}\;{\rm{fm}}\]

Apply the formula:

Substitute the values and determine the velocity as:

\[\begin{array}{l}v = \frac{{6.62 \times {{10}^{ - 34}}{\rm{\;kg}} \cdot {{\rm{m}}^{\rm{2}}} \cdot {\rm{s}}}}{{{\rm{(0}}{\rm{.400\;kg)}}\left( {{\rm{7}}{\rm{.50}} \times {\rm{1}}{{\rm{0}}^{ - {\rm{2}}}}{\rm{\;m}}} \right)}}\\v = 2.21 \times {10^{ - 34}}\;\;\frac{{\rm{m}}}{{\rm{s}}}\end{array}\]

Therefore,the required velocity of the billiard ball is\[{\rm{2}}{\rm{.21}} \times {\rm{1}}{{\rm{0}}^{ - {\rm{32}}}}{\rm{\;}}\;\frac{{\rm{m}}}{s}\].