Now I advise you that start solving the problem in the order that I ask the questions. Neglect the electron masses. 1. The mass difference between two isotopes is sometimes just a neutron mass. The spectrometer should separate them very welI. For such an Isotope combination, the difference in radius should be around 1 cm. That is r - =1 cm. In order to achieve this, choose a magnetic field with a magnitude in Tesla (maximum magnetic field you can obtain from a 15 conventional magnet is around 2.5 T so be far away from this value) and choose the direction also. Then determine the velocity of isotope you need. Last calculate radius r of a Ph, smallest isotope. 2. In order to produce this magnetic field, determine the current and number of turns, radius and other parameters of a solenoid you need. Also show how you will position this solenoid. 10

Now I advise you that start solving the problem in the order that I ask the questions. Neglect the electron masses. 1. The mass difference between two isotopes is sometimes just a neutron mass. The spectrometer should separate them very welI. For such an Isotope combination, the difference in radius should be around 1 cm. That is r - =1 cm. In order to achieve this, choose a magnetic field with a magnitude in Tesla (maximum magnetic field you can obtain from a 15 conventional magnet is around 2.5 T so be far away from this value) and choose the direction also. Then determine the velocity of isotope you need. Last calculate radius r of a Ph, smallest isotope. 2. In order to produce this magnetic field, determine the current and number of turns, radius and other parameters of a solenoid you need. Also show how you will position this solenoid. 10

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Expert Solution

Step 1

Since we only answer up to 1 question, we’ll answer the 1st question only. Please resubmit the question and specify the other question you’d like answered.

Given: Diffrenece in radius $r_{2} - r_{1} = 1 c m = 0.01 m$

Difference in mass $m_{2} - m_{1} = m a s s o f n e u t r o n$

Magnetic field, $B = 2.5 T$ direction is in or out of page (+z or -z )

$q = 82 e$

Step 2

Solution: Radius of circle by a charged particle inside magnetic field is calculated by

$r = \frac{m v}{q B}$

For $P b_{205}$

$r_{2} = \frac{m_{2} v}{q B}$

Now, for $P b_{204}$

$r_{1} = \frac{m_{1} v}{q B}$

Subtracting r₁from r₂

$\begin{array}{rcl} r_{2} - r_{1} & = & (m_{2} - m_{1}) \frac{v}{q B} \\ 0.01 m & = & (1.67 \times 10^{- 27} k g) \times \frac{v}{82 (1.6 \times 10^{- 19} C) (2.5 T)} \\ v & = & \frac{0.01 m \times 82 (1.6 \times 10^{- 19} C) (2.5 T)}{(1.67 \times 10^{- 27} k g)} \\ v & = & 1.96 \times 10^{8} m . s^{- 1} \end{array}$

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