I'm reading an online PDF book about QM, and it starts off with basic experiments, like double slit and photoelectric effect.

At the end of the chapter, there are a couple of simple questions and I need to see if I'm doing them correctly.

 

Book:

http://arxiv.org/pdf/1007.4184v1.pdf

 

Chapter 1, 1.6 Conclusion, question 4:

" You are doing the double-slit experiment with electrons. The distance between the
slits is 1 cm, and the impact screen is at 1 meter from the slits. What speed should
the electrons have in order to obtain an interference pattern with the bright bands
separated by 0.1 m? (The mass of an electron is m_e = 9.11 × 10⁻³¹ kg.)"

 

Now, there's an equation for constructive interference that goes like this:

x = nλL / d,

with x being position on detection screen, like on page 27.

λ being wavelength of electrons,

L being distance between slits and

d being distance to the detection screen from the slits,

and n being a whole integer.

 

I solved above equation for λ and equation m_e × V_e = h / λ for λ and then equalized these two equations, but this x is the problem.

Is that x what distance between bright bands will be? If so, then my result is 0.687 m/s for V_e.

 

I'm aware that I could be very wrong.

Edited December 10, 201213 yr by okr491

Now, there's an equation for constructive interference that goes like this:

x = nλL / d,

with x being position on detection screen

...

 

Is that x what distance between bright bands will be? If so, then my result is 0.687 m/s for V_e.

 

_{Yes. x is the position of bright bands for different values of n}

OK, thanks swansont.