A crystal is grown by evaporating A and 8 type
atoms, and then letting them condense to
form the crystal. If, because of the forces
involved, on A atom is twice as likely to stick to
the crystal OS a B atom, what is the probability
that the final crysta
pls show step i dont know
To find the probability that the final crystal contains A atoms, we need to understand the process of crystal growth described in the question.
1. Starting point: We have two types of atoms, A and B, evaporating and then condensing to form the crystal.
2. Given: The probability of an A atom sticking to the crystal is twice as likely as a B atom.
To solve this problem, we'll calculate the probability of a single atom sticking to the crystal, and then use it to find the probability of the final crystal containing A atoms.
Let's denote the probability of an A atom sticking to the crystal as P(A). Since the probability of an A atom sticking is twice as likely as a B atom, we can say:
P(A) = 2 * P(B)
To find the value of P(A), we need to determine the total probability of the system, which includes both A and B atoms.
The total probability is the sum of the probabilities of all possible outcomes. Since we have two types of atoms (A and B), the total probability can be expressed as:
Total Probability = P(A) + P(B)
However, we also know that the total probability must add up to 1 (100%), as the probability of getting either A or B is certain. Therefore, we can write:
1 = P(A) + P(B)
Now, let's substitute the relationship we determined earlier (P(A) = 2 * P(B)) into the equation:
1 = 2 * P(B) + P(B)
Multiplying P(B) by 2:
1 = 3 * P(B)
Now we can solve for P(B):
P(B) = 1/3
Since we know that P(A) is twice as likely as P(B), multiplying P(B) by 2 gives us:
P(A) = 2 * (1/3)
P(A) = 2/3
Therefore, we have found that the probability of an A atom sticking to the crystal is 2/3 (or 0.67), and the probability of a B atom sticking is 1/3 (or 0.33).
To calculate the probability that the final crystal contains A atoms, we need to know the number of A and B atoms initially present. If we assume an equal number of A and B atoms, the probability of the final crystal containing A atoms can be given by:
P(Final Crystal contains A atoms) = P(A) * P(A) * ... (repeated n times)
Since the number of atoms is not specified in the question, we cannot determine an exact probability value without that information.