Question

Energetic particles, such as protons, can be detected with a silicon detector. When a particle strikes a thin piece of silicon, it creates a large number of free electrons by ionizing silicon atoms. The electrons flow to an electrode on the surface of the detector, and this current is then amplified and detected. In one experiment, each incident proton creates, on average, $35,000$electrons; the electron current is amplified by a factor of $100$; and the experimenters record an amplified current of $3.5\mu \mathrm{A}$. How many protons are striking the detector per second?

Short answer

The number of protons that are striking the detector per second is$6.25million.$

Step-by-step solution

Given Information

Number of electrons$=35,000$

Amplified by a factor $=100$

Amplified current$=3.5\mu A$

Explanation

In this case, $n_p$is the number of protons falling per second.

An elementary charge of $e$equals a proton current of $n_{p}e$.

This current will be measured by multiplying it by the silicon sheet multiplication factor (let it be $m_s$), then multiplying it by the amplification factor (let it be $m_a$).

That is,

$I=n_{p}e{m}_s{m}_a$

As a consequence, it is obvious that protons will flow at a relatively high rate

$n_p=\frac{I}{e{m}_s{m}_a}$

Substitute the expression,

role="math" localid="1649074071828" $n_p=\left(\frac{3.5\times {10}^{-6}A}{1.6\times {10}^{-19}C\times 35000e\times 100}\right)$

$=6.25\times {10}^6.$

Final Answer 

Hence, the number of protons that are striking the detector per second is$6.25million.$