Problems involving electromagnetism

[21385]

Homework Statement

In problems involving electromagnetism it is often convenient and informative to express answers in terms of a constant, x, which is a combination of the Coulomb constant, k, the charge of an electron, e, and H=h/(2pi), with h being Planck's constant. For instance, the lowest energy that a hydrogen atom can have is given by E=-(0.5)(x^2)m(c^2), where m is the mass of the electron and c is the speed of light. Which of the following is the correct expression for x?
(HINT: Non-relativistic kinetic energy is (0.5)m(v^2), where v is the speed.)

a) (k(e^2))/(Hc)
b) H/(k(e^2)c)
c) (k(e^2)H)/c
d) (k(e^2)c)/H

Homework Equations

E=hf
E=m(c^2)
E=(1/2)m(v^2)

The Attempt at a Solution

I really don't know what they are asking for or what formula they are referring. Can someone help? Thanks.

 

[Saketh]

Analyze the units of the various answers (dimensional analysis) in order to get the given expression to be in joules.

You can avoid solving for the energy levels of the hydrogen atom if you use dimensional analysis.

 

[m2003]

I would first clarify the question and make sure I understand what is being asked. It seems that the question is asking for the correct expression for a constant, x, which is used in problems involving electromagnetism. The given equation, E=-(0.5)(x^2)m(c^2), suggests that x is a combination of k, e, and H.

Using the given equations, we can rearrange and substitute to find the correct expression for x. Starting with E=m(c^2), we can substitute in the equation for non-relativistic kinetic energy, E=(1/2)m(v^2), to get m(c^2)=(1/2)m(v^2).

Next, we can rearrange the equation for non-relativistic kinetic energy, E=(1/2)m(v^2), to solve for v^2. This gives us v^2=2E/m.

Substituting this into our original equation, E=-(0.5)(x^2)m(c^2), we get E=-(0.5)(x^2)m(2E/m). Simplifying, we get E=-x^2E.

Finally, we can rearrange this equation to solve for x, giving us x=sqrt(-E/E).

Now, we can substitute in the given values for E, m, and c to find the correct expression for x. This gives us x=sqrt(-(0.5)(k(e^2))(H/(2pi))/(0.5)(m)(c^2)). Simplifying, we get x=sqrt(-(k(e^2)H)/(4pi^2m)).

Therefore, the correct expression for x is (k(e^2)H)/c. Option c is the correct answer.