Question

Relationship between KE and de-broglie's wavelength

Answer 1

In relating a particle's energy to its wavelength, two equations are used. The first is the kinetic energy equation:

Equation Number One: KE = (1/2) mv2



There are three symbols in this equation:

a) KE stands for kinetic energy 
b) m stands for mass 
c) v stands for velocity

I would like to emphasize that these are symbols, which are standing in place of the actual numerical values. Another example of an equation using symbols is PV = nRT. I would also like to emphasize that these symbols are not the units. For example, the symbol P stands for the pressure and the unit on the numerical value for pressure is atm.

Next, some comments on the units attached to the numerical values represented by the symbols in the kinetic energy equation.

The unit on mass is kilograms. That means, if you get a mass in grams given in the problem, you must convert it to kilograms.

The unit on velocity is meters per second, most usually written m s¯1 (it can also be written m/s). One possible point of confusion: The unit m means meters, the symbol m means mass. You have to keep the two separate.

The unit on KE is kg m2 s¯2. Remember that the velocity (symbol = v) is squared. That means the unit (m/s) gets both the length (unit = m, meaning meters) and the time (unit = s, meaning seconds) get squared.

Here's one last confusing thing to make you feel better: the name (as opposed to the symbol) of the KE unit is Joule.

You really do need to keep the difference between a symbol and a unit clear in your mind.

Now, let's manipulate the KE equation. I'm going to use E instead of KE:

E = (1/2) mv2

2E = mv2

2Em = m2v2

2Em = (mv)2

Here's a key point from physics: mv is a particle's momentum. The standard symbol for momentum is p:

2Em = p2

p = √(2Em)

Answer 2

heya @user
here is your answer in the given attachment

hope helped !!
cheers☺ ☺