Mass Spectroscopy, Photoelectric effect, Bohr atom (check over my work please)

[alexlee33]

I have a take home quiz here and it would be greatly appreciated if someone could check over my work (it's numeric response btw):

1) A singly charged lithium ion (m= 1.16x10^-26 kg) is accelerated from rest thru a potential difference of 5.60 x 10^5 V. The velocity selector consists of an electric field (|E|= 4.98 x 10^5 V/m) and a magnetic field. The lithium ion finally enters a magnetic field (B= 0.650 T) perpendicular to it in the ion separation region.

a) What is the energy of the ion?

Ep = Ek
Ep = qV
Ep = (1.6 x 10^-19)(5.6 x 10^5)
FINAL ANSWER: 8.96 x 10^-14

b) What is the magnitude of the magn. field in the velocity selector if the ion remains undeflected?

Fe = Fm
q|E| = qvB
|E| / v = B

To find velocity...
qV = 0.5mv^2
v = (square root)((2(1.6x10^-19)(5.6x10^5) / (1.16x10^-26))
v = 3.93 x 10^6 m/s

Back to |E| / v = B...
(4.98x10^5) / (3.93x10^6) = B
FINAL ANSWER: 0.127 T

c) What is the lithium's radius of deflection in the ion separation region?

r = mv / qB
r = ((1.16x10^-26)(3.93x10^6)) / ((1.6x10^-19)(.65))
FINAL ANSWER: 0.438 m

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2. In a photoelectric cell the minimum voltage req. to reduce the current thru the cell to zero is 8.3 volts. Whats the max speed of the electrons ejected from the photoelectric surface in this cell?

Ep = Ek
qV = 0.5mv^2
v = (square root)((2(1.6x10^-19)(8.3) / (9,11x10^-31))
FINAL ANSWER: 1.7 x 10^6 m/s

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3. X-rays with a min. wavelength of 5.12 x 10^-10 m are produced by an xray tube. Whats the pot. diff. used in operating this tube?

qV = hc / (wavelength)
V = hc / q(wavelength)
V = ((6.63x10^-34)(3x10^8)) / ((1.6x10^-19)(5.12x10^-10))
FINAL ANSWER: 2.43 x 10^3 V

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4. If the 2nd energy level of a hydrogen-like atom is -2.44 x 10^-18 J, what is the energy of the 4th level?

En = E1 / n^2
Find E1... blah blah... do equation again using found E1...
FINAL ANSWER: -6.10 x 10^-19 J

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Thanks! :D

 

[anathema]

Hello there! Thank you for sharing your work with us. I have reviewed your answers and they all seem to be correct. Great job on using the correct equations and units in your calculations. Just a small note, in question 4, the energy of the 4th level should be -6.10 x 10^-20 J instead of -6.10 x 10^-19 J. Keep up the good work!

 

[ogb p]

Great job on your calculations! Here are some comments and suggestions to improve your work:

1) For part a), you have correctly calculated the potential energy of the ion. However, you should also include the kinetic energy in your final answer, as the question asks for the total energy of the ion. So the final answer should be 8.96 x 10^-14 J, not just the potential energy.

2) For part b), your calculation for the velocity is correct, but you have made a mistake in converting the velocity to meters per second. The correct conversion is 3.93 x 10^5 m/s, not 3.93 x 10^6 m/s. This will change your final answer for the magnitude of the magnetic field to 0.0127 T.

3) For part c), your calculation for the radius of deflection is correct, but the units are incorrect. The radius should be in meters, not millimeters. So the final answer should be 0.438 mm, not 0.438 m.

4) For question 2, the answer should be in units of electron volts (eV) and not meters per second. So the final answer should be 1.7 eV, not 1.7 x 10^6 m/s.

5) For question 3, the answer should also be in units of electron volts (eV). So the final answer should be 2.43 x 10^3 eV, not 2.43 x 10^3 V.

6) For question 4, the energy levels of a hydrogen-like atom are given by En = -13.6 eV / n^2. So the energy of the 4th level should be -1.51 eV, not -6.10 x 10^-19 J.

Overall, your calculations are correct, but be sure to double check your units and conversions to ensure accurate final answers. Keep up the good work!