Why c needs to be added in numerator and denominator while solving a de Broglie equation word

Jaylene Duarte

Jaylene Duarte

Answered question

2022-05-14

Why c needs to be added in numerator and denominator while solving a de Broglie equation word problem?
Calculate the de Broglie wavleength of a 0.05 eV ("theremal") neutron.Making a nonrelativistic calculation,
λ = h p = h 2 m 0 K = h c 2 ( m 0 c 2 ) K = 12.4 × 10 3 e V Å 2 ( 940 × 10 6 e V ) ( 0.05 e V ) = 1.28 Å
I am confused as to why it is necessary to add c in the numerator and denominator (red equation) while solving a word problem like this?

Answer & Explanation

TettetoxDetnhte5

TettetoxDetnhte5

Beginner2022-05-15Added 15 answers

The key observation is that the thermal energy is given in eVs. Hence for simplicity it makes sense to convert the mass to its equivalent in eVs by inserting a c / c factor. The value of h c in eV × A is also easy to look up making the entire expression easy to simplify since all energies are in eVs.
The alternative would be to convert the 0.05 eVs to Joules and use throughout numerically small values for K, m and h when these are expressed in the usual metric units. Using eVs and Angstrom avoids avoids such numerically small quantities.
fetsBedscurce4why1

fetsBedscurce4why1

Beginner2022-05-16Added 2 answers

It is not necessary to add c, it is just useful in order to check quickly the dimensions, easily recognize quantities and get the numerical value of the formula faster. This is done often in Physics formulas and it is a very advisable and good habit. In your case, you recognize that multiplying by c both in the numerator and the denominator you get h c and m 0 c 2 which have familiar dimensions, respectively
[ h c ] = [ Energy ] [ Length ] [ m c 2 ] = [ Energy ]
so that it is very easy to see that you end with a length in the formula. Otherwise, you would have managed h which is an energy per time and m that is a mass, making the check of the dimension slightly more involved (or slower). In this way finally you have just to substitute the tabulated values in the correct dimensions.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Quantum Mechanics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?