A mass spectrometer is designed to separate protein fragments. The fragments are ionized by removing a single electron and then enter a 0.80 T uniform magnetic field at a speed of 2.3 * 10^5 m/s.
If a fragment has a mass that is 85 times the mass of the proton, what will be the distance between the points where the ion enters and exits the magnetic field?
A small turtle moves at a speed of 528 furlongs per fortnight. Find the speed of the turtle in centimeters per second. Note that 1 furlong = 220 yards and 1 fortnight = 14 days.
To calculate the distance between the points where the ion enters and exits the magnetic field, we can use the principles of the Lorentz force and centripetal force acting on a charged particle moving in a magnetic field.
Here's how to do it step by step:
Step 1: Find the charge of the ion.
Since the ion is formed by removing a single electron, it carries a positive charge equal to the charge of an electron, which is 1.6 * 10^-19 C.
Step 2: Find the velocity of the ion.
The given velocity of the ion is 2.3 * 10^5 m/s.
Step 3: Calculate the magnetic field radius.
The centripetal force acting on a charged particle moving perpendicular to a magnetic field is given by the equation F_c = (mv^2)/r, where F_c is the centripetal force, m is the mass of the ion, v is its velocity, and r is the radius of its circular path.
Since the ion is traveling in the field at a constant velocity, the magnetic force acting on it must equal the centripetal force: F_m = F_c.
The magnetic force is given by the equation F_m = qvB, where q is the charge of the ion, v is its velocity, and B is the magnetic field strength.
Setting these two forces equal to each other, we get qvB = (mv^2)/r. Rearranging the equation gives us r = (mv) / (qB).
Step 4: Find the mass of the ion.
The mass of the ion is 85 times the mass of the proton, which is approximately 1.67 * 10^-27 kg. Therefore, the mass of the ion is (85 * 1.67 * 10^-27 kg).
Step 5: Calculate the distance between the points.
Substituting the values into the equation r = (mv) / (qB), we can calculate the radius of the circular path. Since the ion enters and exits at different points, we can double the radius to find the distance between the points of entry and exit.
r = (m * v) / (q * B)
r = (85 * 1.67 * 10^-27 kg * 2.3 * 10^5 m/s) / (1.6 * 10^-19 C * 0.80 T)
r ≈ 1.65 * 10^-3 m
Finally, to find the distance between the points where the ion enters and exits the magnetic field, we multiply the radius by 2:
Distance = 2 * r
Distance ≈ 2 * 1.65 * 10^-3 m
Distance ≈ 3.3 * 10^-3 m
Therefore, the distance between the points where the ion enters and exits the magnetic field is approximately 3.3 * 10^-3 meters.