Finding de Broglie wavelength from energy

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robertjford80
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Homework Statement



Textbook page showing equations 1.7 and 1.8 for de Broglie wavelength: lambda = h/sqrt(2mE), and lambda = sqrt(1.5/E) nm with E in electron volts, with surrounding explanatory text.




The Attempt at a Solution



I don't see how they got sqrt(1.5/E) I tried it like this

Square root of 6.62×10^-34 divided by the square root of 2×9.11×10^-31, written as a fraction inside a radical.


Not the right answer.
 
robertjford80 said:

Homework Statement



Textbook page with de Broglie wavelength equations: epsilon = mc^2 + E, lambda = h / sqrt(2mE) (Eq. 1.7), and lambda = sqrt(1.5/E) nm (Eq. 1.8) for an electron with E in electron volts.

The Attempt at a Solution



I don't see how they got sqrt(1.5/E) I tried it like this

Equation: square root of (6.62 × 10^-34 divided by the square root of (2 × 9.11 × 10^-31)), shown in white text on a dark background.


Not the right answer.

It looks like you took the square root of h/(√2m) when you should have done the exact opposite: you should have squared it. Here's the reason. If:$$\sqrt{1.5} = \frac{h}{\sqrt{2m}}$$then$$1.5 = \frac{h^2}{2m}$$

I computed h^2/(2mE), and I plugged in a value of E = 1 so that I would get the same numerical answer as they did. I also had Google express it in nm^2 instead of m^2, so that the answer would be the same as theirs:

Google Calculator link