Answer

Verified

399.3k+ views

**Hint:**In this question, we will proceed by finding all the values in SI units included in the given data. In order to directly get the required result, we will use a simple formula.

Formula Used: We will use the following formula for the kinetic energy acquired by a charge when it is revolving between the dees

${\text{KE}} = 2NqV$

**Complete Step-by-Step Solution:**

The following information is provided to us in the question

The applied magnetic field, $B = 2T$

The potential difference, $V = 100{\text{KV}} = 100 \times 1000\;{\text{V}} = {10^5}\;{\text{V}}$

The kinetic energy to be acquired is given as ${\text{KE}} = 20{\text{MeV}} = 20 \times {10^6}{\text{eV}}$

Where

$e = 1.6 \times {10^{ - 19}}{\text{C}}$(charge of a proton)

So, we get

${\text{KE}} = 20 \times {10^6} \times 1.6 \times {10^{ - 19}}\;{\text{V}}$

Now, we will use the formula listed above

${\text{KE}} = 2NqV$

By substituting the values of the kinetic energy, charge and the potential difference in the above equation, we get

$ \Rightarrow 20 \times {10^6} \times 1.6 \times {10^{ - 19}} = 2N\left( {1.6 \times {{10}^{ - 19}}} \right){10^5}$

$ \Rightarrow N = \dfrac{{20 \times {{10}^6} \times \left( {1.6 \times {{10}^{ - 19}}} \right)}}{{2\left( {1.6 \times {{10}^{ - 19}}} \right){{10}^5}}}$

Upon further solving, we get

$\therefore N = 100$

**So, \[100\] revolutions are required to acquire a kinetic energy of \[20 MeV\]**

Hence, the correct option is (A.)

Hence, the correct option is (A.)

**Additional Information:**A cyclotron is a type of accelerator for compact particles that produces radioactive isotopes that can be used for imaging procedures. In a magnetic field, stable, non-radioactive isotopes are placed into the cyclotron, which accelerates charged particles (protons) to high energy.

**Note:**In this specific problem, an additional data is given, i.e., the magnitude of the magnetic field equal to \[2 T\]. To solve this issue, this information is not at all necessary. The units should be taken care of in these types of challenges. In order to ensure the units' transparency, we converted kilovolts into volts and MeV into volts.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

10 examples of evaporation in daily life with explanations