Matter & Photon Particle Comparison

[HarleyM]

Homework Statement

Compare and contrast a 2.2 eV photonn with a 2.2 eV electron in terms of energy(J), rest mass (Kg) speed (m/s) wavelength (m) and momentum kgm/s.

Homework Equations

For Photon
P=E/C
F=E/h
V=fλ
λ= h/P

For Electron
λ=h/mv
m=E/C²
p=h/λ
Ke=1/2mv²

The Attempt at a Solution

Photon
2.2 ev X 1.6x10^-19= 3.52 x10 ^-19 J

P=E/C
P= 3.52 x10 ^-19 / 3 x 10⁸
P= 1.17 x10 ^-27

f= E/h
=3.52 x10 ^-19 /6.63x10^-34
F=5.31x10¹⁴

v=fλ
v= 3x10⁸ m/s

λ= h/P
=6.63X10^-34/1.17X10^-27
=5.66X10^-7 m

m=? ( Does a photon have a rest mass?) I don't think a photon has a rest mass.

Electron

2.2 eV x1.6x10^-19 = 3.52 x 10^-19 J

Should rest mass be the standard 9.11 x10^-31 kg

Or should I calculate using E=mc²

m= E/C²
m= 3.52 x 10^-19 / (3x10⁸)²
m=3.91 x10 ^-36 kg


( I use 9.11 x10^-31 kg as the mass for the rest of the calculations but I can change it if its incorrect and the calculated mass should be used! )


Ek=1/2mv²
3.52 x 10^-19=1/2 (9.11x10^-31)v²
v= √[(3.52 x 10^-19)(2)/9.11x10^-31]
v=8.79x10⁵ m/s ( Unsure whether I can use this equation to determine speed)

λ=h/mv
= 6.63x10^-34/(9.11X10^-31)(8.79X10⁵)
=8.28X10^-10 m

p= h/λ
=6.63x10^-34/8.28X10^-10
=8x10^-25 kgm/s

Parts I have highlighted is where I am unsure! Thanks for all the help!

If I have misused any equations ( i.e used matter equations for light or vice versa can you please alert me! )

 

[Curious3141]

The Attempt at a Solution

Photon
2.2 ev X 1.6x10^-19= 3.52 x10 ^-19 J

Correct. I didn't check your numbers, but make sure you don't round off your physical constants and intermediate results too early so that you have adequate precision for your final answer.

P=E/C
P= 3.52 x10 ^-19 / 3 x 10⁸
P= 1.17 x10 ^-27

Correct. You're missing the units though.

f= E/h
=3.52 x10 ^-19 /6.63x10^-34
F=5.31x10¹⁴

Why bother? They didn't ask for the frequency.

v=fλ
v= 3x10⁸ m/s

Just quote v = c (then the numerical value as you did).

λ= h/P
=6.63X10^-34/1.17X10^-27
=5.66X10^-7 m

Correct. I didn't check your numerical computation, but make sure you don't have an error in your last few significant digits (because you rounded off the previous answer).

m=? ( Does a photon have a rest mass?) I don't think a photon has a rest mass.

You're right, photons have no rest mass. Answer is 0.

Electron

2.2 eV x1.6x10^-19 = 3.52 x 10^-19 J

Correct.

Should rest mass be the standard 9.11 x10^-31 kg

Or should I calculate using E=mc²

No. Rest mass is just the standard constant. It doesn't change.

m= E/C²
m= 3.52 x 10^-19 / (3x10⁸)²
m=3.91 x10 ^-36 kg

Unnecessary. You are actually calculating the apparent gain in mass due to kinetic energy. Note that this is small relative to the rest mass (error of 4 parts per million or so).

( I use 9.11 x10^-31 kg as the mass for the rest of the calculations but I can change it if its incorrect and the calculated mass should be used! )

No, use the rest mass.

Ek=1/2mv²
3.52 x 10^-19=1/2 (9.11x10^-31)v²
v= √[(3.52 x 10^-19)(2)/9.11x10^-31]
v=8.79x10⁵ m/s ( Unsure whether I can use this equation to determine speed)

You can, since the electron is clearly traveling at speeds significantly less than c. So relativistic effects don't matter. I didn't check your computation, but the principle is right.

λ=h/mv
= 6.63x10^-34/(9.11X10^-31)(8.79X10⁵)
=8.28X10^-10 m

Looks right.

p= h/λ
=6.63x10^-34/8.28X10^-10
=8x10^-25 kgm/s

You can just do p = mv, which you calculated as the denominator in the previous part.

 

[HarleyM]

Wow very concise answer, thank you very much

WOOO i get physics, its a great feeling