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I need help understanding this problem. These are the correct answers I just need a break down of how to get them.
**Problem Five.** A biologist is studying the effects of alpha radiation as it impacts skin cells. Alpha particles are the nuclei of helium atoms (two protons and two neutrons). She uses ionized helium gas (where electrons have been separated from the helium nuclei). The ionized gas is injected into the **mass spectrometer** shown below. First, the gas enters the **“velocity selector”** chamber on the left where there is a uniform electric field and uniform magnetic field. Here the energy of the alpha particles will be determined by selecting their velocity. After passing through the **“velocity selector”** chamber, the particles pass through a hole into the **“charge/mass selector”** chamber where the alpha particles follow the circular trajectory shown and are emitted from point P where they impact the skin cells. ![Diagram Explanation] A diagram on the right shows a mass spectrometer setup. On the left, a rectangular section labeled **“Velocity selector”** indicates where the electric field, \(E\), and magnetic field, \(B_1\), are present. A vector \( \vec{v} \) indicates the velocity. On the right, a semicircular section labeled **“Charge/mass selector”** indicates where \(B_2\) is present. Point **P** is marked at the end of the semicircular path. **15.** The biologist would like to use alpha particles that have speed \( v = 2.12 \times 10^8 \, \text{m/s} \). The magnetic field \( B_1 \) inside the **“velocity selector”** is \( 3.00 \, \text{mT} \) pointing into the page. Find the magnitude of the magnetic force \( \vec{F}_1 \) (in units of \( 10^{-13} \, \text{N} \) ) on the alpha particles. - (A) 4.58 - (B) 3.56 - (C) 4.32 - (D) 2.04 - (E) 5.56 **16.** What direction must the biologist choose for the electric field \( \vec{E} \) in the **“velocity selector”** chamber to keep the particles moving in a straight line? - (A) Up - (B) Down - (C) Left - (
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Transcribed Image Text:**Problem Five.** A biologist is studying the effects of alpha radiation as it impacts skin cells. Alpha particles are the nuclei of helium atoms (two protons and two neutrons). She uses ionized helium gas (where electrons have been separated from the helium nuclei). The ionized gas is injected into the **mass spectrometer** shown below. First, the gas enters the **“velocity selector”** chamber on the left where there is a uniform electric field and uniform magnetic field. Here the energy of the alpha particles will be determined by selecting their velocity. After passing through the **“velocity selector”** chamber, the particles pass through a hole into the **“charge/mass selector”** chamber where the alpha particles follow the circular trajectory shown and are emitted from point P where they impact the skin cells. ![Diagram Explanation] A diagram on the right shows a mass spectrometer setup. On the left, a rectangular section labeled **“Velocity selector”** indicates where the electric field, \(E\), and magnetic field, \(B_1\), are present. A vector \( \vec{v} \) indicates the velocity. On the right, a semicircular section labeled **“Charge/mass selector”** indicates where \(B_2\) is present. Point **P** is marked at the end of the semicircular path. **15.** The biologist would like to use alpha particles that have speed \( v = 2.12 \times 10^8 \, \text{m/s} \). The magnetic field \( B_1 \) inside the **“velocity selector”** is \( 3.00 \, \text{mT} \) pointing into the page. Find the magnitude of the magnetic force \( \vec{F}_1 \) (in units of \( 10^{-13} \, \text{N} \) ) on the alpha particles. - (A) 4.58 - (B) 3.56 - (C) 4.32 - (D) 2.04 - (E) 5.56 **16.** What direction must the biologist choose for the electric field \( \vec{E} \) in the **“velocity selector”** chamber to keep the particles moving in a straight line? - (A) Up - (B) Down - (C) Left - (
Expert Solution
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Step 1: 15. To find the magnitude of the magnetic force on the alpha particle.

Given that 

Speed of alpha particle,v equals 2.12 cross times 10 to the power of 8 m divided by s

Magnietic field,B equals 3 space m T equals 3 cross times 10 to the power of negative 3 end exponent T

The magnitude of the magnetic force on the alpha particle

F subscript 1 equals q open parentheses v cross times B close parentheses space space space space equals 2 e open parentheses v cross times B close parentheses space space space space equals 2 cross times 1.6 cross times 10 to the power of negative 19 end exponent cross times open parentheses 2.12 cross times 10 to the power of 8 cross times 3 cross times 10 to the power of negative 3 end exponent close parentheses space space space space bold equals bold 2 bold. bold 04 bold cross times bold 10 to the power of bold minus bold 13 end exponent bold italic N

Hence, the correct option is D.

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