Amass spectrometer is being used to separate common oxygen-16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (the relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice was deposited.) the ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.66 x 10^-26 kg, and they are both singly charged and travel at 5.15 x 10^6 m/s in a 1.2 t magnetic field. what is the separation between their paths when they hit a target after traversing a semicircle? show all steps

The path separation is 0.089 m

Solution:

As per the question:

Mass of , m = 2.66\times 10^{- 26}\ kg[/tex]

Ratio of the masses of to , R = 16:18

Velocity of the masses, v =

Magnetic field, B = 1.2 T

Now,

The separation between the path after completing a semicircle can be calculated as:

Mass of , m' = mR =

Here, magnetic force provides the necessary centripetal force to traverse the semi-circle:

where

= Magnetic force

q = e = electronic charge =

v = Velocity

B = Magnetic field

r = Radius

Now, the radius from the above eqn comes out to be:

Now, for

Now, for

Now, the path separation is given by:

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: