In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack.

(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?

(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?

 

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In a game of billiards a player wishes to sink a target ball in a corner pocket. If the angle to the corner pocket is 35 degrees, at what angle is the cue ball deflected. Assume that friction and rotational motion are unimportant and that the collision is elastic. Also assume that billiard balls have the same mass.

 

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In a game called Taxation and Evasion, a player rolls a dice. If on any turn the sum is 3, or 4, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dicea. What distribution should be used to describe the outcomes of this game? What is the probability that she does not get audited? What is the probability that she gets audited at least once? What is the probability that she gets audited no more than 2 times? What are the variance and the standard deviation of the number of times she will be audited?

 

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The diagrams below represent different states in the fusion process:

A proton (1H nucleus) and a deuteron (2H nucleus) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3 nucleus and a gamma ray (a high energy photon, which has kinetic energy but zero rest energy). Consider the system containing all particles. Work out the answers to the following questions on paper, using symbols (algebra), before plugging numbers into your calculator.

A: Bringing the particles together

Which diagram depicts the initial state in the process of bringing the particles together?

cba

Which diagram depicts the final state in the process of bringing the particles together?

cab

Compare the initial state and final states of the system. Which quantities have changed?

kinetic energyrest energypotential energy

The deuterium nucleus starts out with a kinetic energy of8.4e-14joules, and the proton starts out with a kinetic energy of1.67e-13joules. The radius of a proton is 0.9e-15 m; assume that if the particles touch, the distance between their centers will be twice that. What will be the total kinetic energy of both particles an instant before they touch?

joules

B: Reaction to make heliumNow that the proton and the deuterium nucleus are touching, the reaction can occur.

Take the final state from the previous process to be the initial state of the system for this new process.

Which diagram depicts the final state?

abc

Compare the initial state and final states of the system. Which quantities have changed?

potential energykinetic energyrest energy

What is the kinetic energy of the reaction products (helium nucleus plus photon)?

joules

C: Gain of kinetic energy:

What was the gain of kinetic energy in this reaction? (The products have more kinetic energy than the original particles did when they were far apart. How much more?)

joules

D: Fusion as energy source

Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated?

joules

(For comparison, around 1e6 joules are obtained from burning a mole of gasoline.)

 

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In a FRET experiment, the donor GFP (GFP absorbs at 487 nm, emits at 510 nm) is attached to protein A, and the acceptor YFP (YFP absorbs at 514 nm, emits at 535 nm) is attached to protein B. The value of ro is 10Å. a. If protein A does not bind to protein B, fluorescence will be observed at what wavelength?

 

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