Exam exercises: Quantum mechanics

[kaalen]

Hi all! This is my first post... so have mercy on me

We had an exam from computer technologies today and there were only 8 of us loosers who still didn't pass it and no one is sure about the correct solutions:

1.) What is wave frequency of 0,5m long whistle sound? What is the frequency of the next higher tone?

2.) A 20A current runs through a Cu wire with intersection 5mm^2. What is the traveling speed of charge carrying particles in this wire?

3.) We have some light diode which has "forbidden" belt width 3,5eV. What is the wave length of emitted light, energy and momentum of a single photone?

4.) Diode has a saturation current 200microA. Temperature is 140°C and the voltage on diode is 0,5V... what current goes through diode?

5.) Hall's coeficient of a doped silicium at room temperature (25°C) is 0,05Vm/AK. With what kind of dopand is this silicium doped and what is the concentration of dopands?

Extra info:
k_B = 1,38*10^-23J/K
h=6,63*10^-34Js
e_0=1,6*10^-19As
rho_Si=2,33g/cm^3
relative atomic mass of Si = 28
N_A = 6*10^26/kmol
M_Cu = 64kg/mol
rho_Cu = 9 (relative density ) - WTF is relative density supposed to mean?
speed of sound = 340m/s

I'm aware that this must be a horrible translation so I won't wonder if you die laughing like crazy.

1: I didn't have problems with 1. exercise... you just have to know that this is wave motion is "fixed" on one side and "free" on the other. (v_0=170/s, v_1=340/s I hope)

2: It bothered me because I got a very small speed for electrons in my opinon.

3: Didn't have a clue what to do with this E_g (gap energy)... really need help here.

4: No current at all (but I guess it's possible and I'm just used to getting non zero results on exam)

5: I calculated this concentration (n): n = 1/(R_h*e_0) but I don't know if this is overall concentration of all charge carrying particles or just dopands

I'm sorry if I'm asking simple and stupid things... I have serious problems finding any books on these topics in libraries and we didn't do much exercise at school.

 

[kaalen]

anyone... please I really need help here. I asked anyone else I know... but no one had any clue about this sort of physics

 

[quantumdude]

1.) What is wave frequency of 0,5m long whistle sound? What is the frequency of the next higher tone?

It's not possible to tell. Are they asking about the fundamental? The third harmonic? The question doesn't say.

2.) A 20A current runs through a Cu wire with intersection 5mm^2. What is the traveling speed of charge carrying particles in this wire?

It's OK if you get a small speed. Just use the formula that relates current to drift velocity.

3.) We have some light diode which has "forbidden" belt width 3,5eV. What is the wave length of emitted light, energy and momentum of a single photone?

The photon is going to result from a transition from the conduction band (which is just above the forbidden band) to the valence band. That transition has an energy of 3.5 eV.

4.) Diode has a saturation current 200microA. Temperature is 140°C and the voltage on diode is 0,5V... what current goes through diode?

Check out the following website. There's a very conspicuous equation that you need to use.

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/comp/passive/diode/chars/chars.htm

5.) Hall's coeficient of a doped silicium at room temperature (25°C) is 0,05Vm/AK. With what kind of dopand is this silicium doped and what is the concentration of dopands?

I'm not sure about this one, and I'm not near my books to look it up, so let me ask you something. How does your book define each symbol in the equation you used?

 

[kaalen]

It's not possible to tell. Are they asking about the fundamental? The third harmonic? The question doesn't say.

The first question asks about fundamental frequency... sorry I translated it wrong. So the wave length of the fundamental frequency is lambda_0 = L/4 right and lambda_1 = 3*L/4... so... freq_0 = 170/s and freq_1 = 907/s (c = freq * lambda)... Obviously I made some mistake in calculation at exam. But at least I draw correct sketches though this didn't help.

It's OK if you get a small speed. Just use the formula that relates current to drift velocity.

I used this two formulas: n = (rho*N_a)/M and j=I/S = n*e_0*v (v - average velocity) and if you turn this around a little bit you get v = (I*M)/(rho*N_a*e_0*S) = 0,296m/s... but this is sooo slow for electrons

The photon is going to result from a transition from the conduction band (which is just above the forbidden band) to the valence band. That transition has an energy of 3.5 eV.

****... I knew it had to be something very easy... so E_g is equal to photon energy and we know what the speed of light is it's very simple to calculate wave length and momentum... to bad I didn't guess this on exam

Check out the following website. There's a very conspicuous equation that you need to use.

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/comp/passive/diode/chars/chars.htm

Ok, I used the correct formula and got I=0... which is ok. I think the trick was that you had to convert electron volts to joules or vice versa to get the correct exponent.

I'm not sure about this one, and I'm not near my books to look it up, so let me ask you something. How does your book define each symbol in the equation you used?

Unfortunately I don't have any book describing this... only my and professor's notes which only say that this is concentration of charge carrying particles... but I think since Si is a semiconductor you have to think about "holes" as well.


Well... as my professor would say... more luck next time

 

[quantumdude]

The first question asks about fundamental frequency... sorry I translated it wrong.

OK, so you were on the right track with this one.

I used this two formulas: n = (rho*N_a)/M and j=I/S = n*e_0*v (v - average velocity) and if you turn this around a little bit you get v = (I*M)/(rho*N_a*e_0*S) = 0,296m/s... but this is sooo slow for electrons

I've seen smaller drift velocities come up in these types of problems. It's OK.

****... I knew it had to be something very easy... so E_g is equal to photon energy and we know what the speed of light is it's very simple to calculate wave length and momentum... to bad I didn't guess this on exam

That's right.

Ok, I used the correct formula and got I=0... which is ok. I think the trick was that you had to convert electron volts to joules or vice versa to get the correct exponent.

The only way to get zero out of that formula is if V=0, which it doesn't. So you should have found a nonzero current.

Unfortunately I don't have any book describing this... only my and professor's notes which only say that this is concentration of charge carrying particles... but I think since Si is a semiconductor you have to think about "holes" as well.

You should ask the prof for clarification, then.

 

[kaalen]

OK, so you were on the right track with this one.
The only way to get zero out of that formula is if V=0, which it doesn't. So you should have found a nonzero current.

I think I know where I made a mistake... at conversion... for me it vas 1AsV = 1eV... which is wrong 1AsV = 1J Another stupid mistake. Real ****... I could've passed the exam if I weren't so confused.