Question

The de Broglie wavelength of an electron in a hydrogen atom is 1.66 nm.Identify the integer n that corresponds to its orbit.

Answer 1

Answer:

$n=5$

Explanation:

The De Broglie equation is given by:

$\lambda=\frac{h}{mv}$

Where:

• h is the Plank constant $h=6.626*10^{-34}J$
• m is the electron mass $m_{e}=9.1*10^{-31}kg$
• v is the speed of the electron

Then:

$v=\frac{h}{m\lambda}$ (1)

The  energy equation of a hydrogen electron in a orbit n is:

$E=-\frac{R_{H}}{n^{2}}$ (2)

• R(H) is the Rydberg constant $R_{H}=2.18*10^{-18}J$
• n is an integer that corresponds to electron orbit.

We can write E as a kinetic energy an use v of the equation (1)

$\frac{1}{2}mv^{2}=\frac{R_{H}}{n^{2}}$

$n^{2}=\frac{2R_{H}}{mv^{2}}$        

$n=\frac{m\lambda}{h}\sqrt{\frac{2R_{H}}{m}}$      

$n=\frac{9.1*10^{-31}*1.66*10^{-9}}{6.626*10^{-34}}\sqrt{\frac{2*2.18*10^{-18}}{9.1*10^{-31}}}$  

$n=5$

I hope it helps you!