A beam of protons is moving toward a target in a particle accelerator. This

im trying to study for my exam by doing problems, however im stuck with this one. any help is appreciated

beam constitutes a current whose value is 0.39A. (a) How many protons strike the target in 14 seconds? (b) Each proton has a kinetic energy of 3.9 x 10-12 J. Suppose the target is a 14-gram block of metal whose specific heat capacity is 1100 J/(kg Co), and all the kinetic energy of the protons goes into heating it up. What is the change in temperature of the block at the end of 14 s?

a/ use the charge on a proton, knowing an ampere is a coulomb per second.

number=current/chargeproton *timeinseconds

b. Ke total=number*KEeach=mass*c*changetemp
solve for change in temp

To solve this problem, we need to use the formulas related to current, charge, and specific heat capacity.

(a) To calculate the number of protons that strike the target in 14 seconds, we can use the formula:

Number of protons = current × time / charge of a single proton

The charge of a single proton is given by the elementary charge, e = 1.6 x 10^-19 C.

Plugging in the values:

Number of protons = (0.39 A) × (14 s) / (1.6 x 10^-19 C)

Calculating the expression:

Number of protons = 3.465 x 10^18 protons

Therefore, approximately 3.465 x 10^18 protons strike the target in 14 seconds.

(b) To find the change in temperature of the block, we can use the formula:

Change in temperature = (Energy absorbed) / (mass × specific heat capacity)

The energy absorbed by the block is equal to the sum of the kinetic energies of all the protons striking it. Since the kinetic energy of each proton is given as 3.9 x 10^-12 J, the total energy absorbed is:

Energy absorbed = (Number of protons) × (kinetic energy of each proton)

Plugging in the values:

Energy absorbed = (3.465 x 10^18 protons) × (3.9 x 10^-12 J)

Calculating the expression:

Energy absorbed = 1.353 x 10^7 J

The mass of the block is given as 14 grams, which is equivalent to 0.014 kg. Now, we can calculate the change in temperature using the specific heat capacity, given as 1100 J/(kg Co):

Change in temperature = (1.353 x 10^7 J) / (0.014 kg × 1100 J/(kg Co))

Calculating the expression:

Change in temperature ≈ 869.2 degrees Celsius

Therefore, the change in temperature of the block at the end of 14 seconds is approximately 869.2 degrees Celsius.

To find the number of protons that strike the target in 14 seconds, we need to use the formula:

N = I * t / q

where N is the number of protons, I is the current, t is the time, and q is the charge of a proton.

(a) Given that the current is 0.39 A, the time is 14 seconds, and the charge of a proton is 1.6 x 10^-19 C, we can calculate the number of protons that strike the target:

N = 0.39 A * 14 s / (1.6 x 10^-19 C)

To calculate this, divide the product of the current and time by the charge of a single proton. This will give you the number of protons that strike the target.

(b) Now let's move on to the change in temperature of the block of metal. We can use the formula:

ΔQ = m * c * ΔT

where ΔQ is the change in heat energy, m is the mass of the block (14 grams or 0.014 kg), c is the specific heat capacity of the metal (1100 J/(kg Co)), and ΔT is the change in temperature.

We know that the kinetic energy of each proton is 3.9 x 10^-12 J. Therefore, the total heat energy delivered to the block by the protons can be calculated as:

Q = N * E

where Q is the total heat energy, N is the number of protons, and E is the energy of each proton.

Using the values of N and E, we can calculate the total heat energy delivered to the block.

Now, equate ΔQ with Q:

ΔQ = Q

Substituting the equation for ΔQ and Q, we get:

m * c * ΔT = N * E

Rearranging the equation to solve for ΔT:

ΔT = (N * E) / (m * c)

Substituting the values we have, we can find the change in temperature of the block at the end of 14 seconds.

I hope this helps you solve the problem and prepare for your exam!