# Tutor profile: Tyler S.

## Questions

### Subject: Nuclear Physics

Assume we have four cookies. One cookie emits alpha radiation, one beta, one neutron, and one gamma. Choose one cookie with which you would: A) Eat B) Put in your backpack C) Hold in your hand D) Throw away

We would want to hold the alpha emitter in our hand. Although alpha emitters deposit a large amount of energy, they lack the penetrating power and are easily stopped by the dead layer of skin in your hands. Thus, it is safe to hold. We would want to put the beta emitter in our backpack. Beta emitters have slightly more penetrating power compared to alpha emitters, but the leather in your backpack would sufficiently shield you. We want to throw away the neutron emitter. Neither your skin nor backpack would properly shield you from it, and the high water content of the human body would mean a large amount of the neutron's energy would be deposited into your cells. The best strategy is to put as much distance between you and the neutrons as possible so they have more opportunities to interact and thus deposit their energy elsewhere. Lastly, this means we want to eat the gamma emitter. This might seem counter-intuitive at first, but ultimately the penetrating power of gammas is high enough that we would be exposed to its radiation no matter what option we chose. The least dangerous option is to eat the gamma emitter.

### Subject: Nuclear Engineering

Determine the width of lead shielding necessary to attenuate a 1 MeV laser such that the initial intensity of the laser, $$I_{0}$$ is less than 5% of the original intensity.

First, we must look up the mass attenuation coefficient of lead for 1 MeV gamma radiation, the NIST value of which is 7.102E-02 $$\frac{cm^2}{g}$$. Additionally, we must know the density of lead, which is 11.34 $$\frac{g}{cm^3}$$. Plugging this into the Lambert's Law for linear attenuation, $$I(x) = I_{0}e^{-\mu\rho x}$$, where x is in cm, we get $$I(x) = I_{0}e^{-(7.102E-02)(11.34) x}$$. Knowing that $$\frac{I(x)}{I_{0}} = 0.05$$, we can solve for x. Thus, $$x = -\frac{1}{(7.102E-02)(11.34)}\ln{0.05} = 3.72 \ cm$$. Thus, for the intensity of the laser to be less than 5%, we need a lead sheet with a thickness greater than 3.72 cm.

### Subject: Calculus

The volume in liters of water in a tank is defined by the function $$v(t) = 250 - 2\ln(t)$$ for $$0 \leq t \leq 100$$ What is the rate of flow at t = 20?

To find the rate of flow, you need to differentiate the function v(t). Applying our differentiation rules, we find that $$v'(t) = 0 - \frac{2}{t} = -\frac{2}{t} $$. Plugging in t=20, we find the flow rate to be $$v'(t) = -\frac{1}{10} L/s$$

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