do problem 3 please A ping pong ball weighs 2.7 grams and can be moving as fast

Question

do problem 3 please

A ping pong ball weighs 2.7 grams and can be moving as fast as 60mph midflight. What is the deBroglie wavelength of such a ball? What is its kinetic energy? You should be able to do well with a non-relativistic approximation here. b) Now suppose we take the length of a ping pong table L = 274cm as a box and consider the lowest standing wave that can fit within L on the condition that wave amplitude vanishes at the boundaries (see pic below)-this would be the quantum groundstate of the ping pong ball. Compute the ground state energy. c) What are the wavelength and the energy of the next higher solution (again, the idea is that wave's amplitude must vanish at the walls)

Explanation / Answer

formula for debrogile wavelength is

lamda = h/ mv

= 6.63 * 10^-34 /0.0027 ( 60 mph( 0.44704 meters / second/ mph)

=9.15 * 10^-33 m

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lamda = h/ sqrt 2mE

lamda^2 = h^2/ 2mE

E = h^2/ 2m lamda^2

=(6.63 * 10^-34 )^2/ 2( 0.0027) ( 9.15 * 10^-33)^2

=0.9710 J

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