After the velocity selector, a mass spectrometer allows the charged particle to enter a region of magnetic field only, where it follows a curved trajectory and hits a detector which records his position. Your mass spectrometer has the velocity selector set for 2.39 x 10^5 m/s and a magnetic field of 0.1 Tesla. You record particles on the detector 20 cm from the entrance slit. What type of particle have you detected?
1)electron
2)hydrogen ion H+
3)positron
4)helium ion He+
L=0.2 m => R=0.1 m
mv²/R=qvB
q/m= v/RB = 2.39•10⁵/0.1•0.1 =
=2.39•10⁷ C/kg
helium ion He+
q/m= 1.6•10⁻¹⁹/(4•1.67•10⁻²⁷+9.1•10⁻³¹) =2.39•10⁷ C/kg
Thank you very very much
To determine the type of particle detected, we can make use of the principles of the velocity selector and the magnetic field.
The velocity selector is set to a specific velocity, which allows only particles with that velocity to pass through. The equation for the velocity selector is given by:
eV/m = B^2l^2/2
Where:
- e is the charge of the particle
- V is the voltage applied to the velocity selector
- m is the mass of the particle
- B is the magnetic field strength in Tesla
- l is the length of the velocity selector plates
In this case, we are given a velocity selector set for a velocity of 2.39 x 10^5 m/s and a magnetic field strength of 0.1 Tesla.
Plugging these values into the equation, we can solve for eV/m:
(1.6 x 10^-19 C)(2.39 x 10^5 m/s) = (0.1 T)^2 l^2 / 2
According to the given options, we can calculate the value of eV/m for each particle and see which option matches the calculated value.
1) For an electron:
- eV/m = (1.6 x 10^-19 C)(2.39 x 10^5 m/s) ≈ 3.824 x 10^-14 C⋅m/kg
2) For a hydrogen ion H+:
- eV/m = (1.6 x 10^-19 C)(2.39 x 10^5 m/s) ≈ 3.824 x 10^-14 C⋅m/kg
3) For a positron:
- eV/m = (1.6 x 10^-19 C)(2.39 x 10^5 m/s) ≈ 3.824 x 10^-14 C⋅m/kg
4) For a helium ion He+:
- eV/m = (1.6 x 10^-19 C)(2.39 x 10^5 m/s) ≈ 3.824 x 10^-14 C⋅m/kg
Comparing the calculated value of eV/m with the options, we can see that all the options have the same value. Therefore, based on the information provided, we cannot determine the specific type of particle that has been detected.
To determine the type of particle detected in the mass spectrometer, we can use the principles of the mass spectrometer and the known values given.
The mass spectrometer works by applying both an electric field (velocity selector) and a magnetic field to the charged particles. By adjusting the magnetic field strength, only particles with a specific mass-to-charge ratio will follow a curved trajectory and reach the detector.
Given that the velocity selector is set for 2.39 x 10^5 m/s, we can use the formula for the force experienced by a charged particle in a magnetic field:
F = q * (v * B)
Where:
- F is the force exerted by the magnetic field,
- q is the charge of the particle,
- v is the velocity of the particle,
- B is the magnetic field strength.
Since the velocity selector is set for a specific velocity, we can assume that the particle being detected has that velocity (2.39 x 10^5 m/s).
The force experienced by the particle will cause it to curve in the magnetic field and hit the detector. The distance from the entrance slit to the detector is given as 20 cm.
By rearranging the formula for force, we can solve for the charge-to-mass ratio (q/m):
q/m = (F / v) / B
The charge-to-mass ratio is unique for each type of particle. By comparing the calculated charge-to-mass ratio with the known values for different particles, we can determine the type of particle detected.
For the electron (option 1), hydrogen ion (H+ - option 2), and helium ion (He+ - option 4), the charge-to-mass ratios are well-established constants (for a hydrogen ion, the charge is 1e and the mass is approximately 1u, and for an electron, the charge is -1e with a mass of approximately 0.0005u).
By substituting the known values into the formula above and calculating the charge-to-mass ratio, we can compare it with the calculated value.
For the positron (option 3), the charge-to-mass ratio is the same as that of an electron (+1e / 0.0005u) but with a positive charge.
Using this information, we can calculate the charge-to-mass ratio and determine the type of particle detected.