If you could produce a sample containing 2,400,000 free neutrons, what would it be 2658 seconds later?

A) 300,000 neutrons, 2,100,000 protons, and 2,100,000 electrons. MY ANSWER

B) 300,000 neutrons and 2,100,000 protons

C) 300,000 neutrons, 2,100,000 protons, 2,100,000 neutrinos and 2,100,000 electrons.

D) 300,000 neutrons, 300,000 protons, and 300,000 electrons

am I correct

To answer this question, we need to understand the process that occurs over time with a sample containing 2,400,000 free neutrons.

Neutrons can undergo radioactive decay and turn into protons, electrons, and neutrinos. The half-life of a free neutron is around 14 minutes and 42 seconds (882 seconds).

Starting with 2,400,000 neutrons, 2658 seconds later (about 44 minutes), we can calculate the decay that would have occurred.

Using the formula for radioactive decay, we can calculate the number of neutrons remaining:

N = N0 * (1/2)^(t / t1/2)

Where:
N = Final number of neutrons
N0 = Initial number of neutrons
t = Time passed
t1/2 = Half-life of neutrons

Plugging in the values, we get:

N = 2,400,000 * (1/2)^(2658 / 882)
N ≈ 2,400,000 * (1/2)^3 ≈ 300,000 neutrons remaining

So, the correct answer is (B) 300,000 neutrons and 2,100,000 protons.

To determine the correct answer, we need to understand how free neutrons decay over time. Free neutrons have a half-life of approximately 14 minutes and 42 seconds (885 seconds). This means that every 885 seconds, half of the original number of neutrons will decay.

In the given question, we are starting with 2,400,000 free neutrons and waiting for 2658 seconds. To find the number of neutrons remaining after this time, we need to calculate the number of decay cycles that have occurred.

The number of decay cycles is simply the elapsed time divided by the half-life time:

2658 seconds / 885 seconds = 3.0 cycles (rounded to the nearest whole number)

Now, to find the number of neutrons remaining after 3 cycles, we can use the exponential decay formula:

Remaining neutrons = Initial neutrons * (1/2) ^ number of cycles

Plugging in the values:

Remaining neutrons = 2,400,000 * (1/2) ^ 3
= 2,400,000 * (1/8)
= 300,000 neutrons

Therefore, the correct answer is A) 300,000 neutrons, 2,100,000 protons, and 2,100,000 electrons. You are correct.