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
No one has answered this question yet.
The half life of a neutron is 10.8 minutes, or 648 seconds, according to one source I found. There seems to be some uncertainty about it, however. 2658 seconds is about 4 half lives. The number of neutrons left will be (1/2)^4 = 1/16 of the original value, or about 150,000. Your book seems to be using a different half life. Anyway, C is the best answer. Each decayed neutron turns into a proton, an electron and a neutrino.
To determine the correct answer, we need to understand the decay process of the neutrons.
Neutrons are unstable particles and undergo radioactive decay, specifically beta decay. During beta decay, a neutron is converted into a proton, an electron, and an antineutrino. This process can be represented by the equation:
n -> p + e- + v̅
Now let's consider the given scenario. Initially, we have 2,400,000 free neutrons. We want to know what the composition of the sample will be 2658 seconds later.
The decay of each neutron occurs independently and at a constant rate. The decay constant for neutrons is typically denoted by λ, and for free neutrons it is approximately 0.693 / τ, where τ is the half-life of neutrons.
The half-life of free neutrons is about 14 minutes (or 840 seconds). Therefore, the decay constant for free neutrons is λ = 0.693 / 840 ≈ 0.0008238 s^-1.
Now, we can calculate the number of remaining neutrons after 2658 seconds using the equation:
N(t) = N(0) * e^(-λt)
where N(t) is the number of neutrons present at time t, N(0) is the initial number of neutrons, e is the base of the natural logarithm (approximately 2.71828), λ is the decay constant, and t is the time in seconds.
Plugging in the values, we have:
N(2658) = 2,400,000 * e^(-0.0008238 * 2658)
Calculating this expression gives us approximately 1,872,297 neutrons remaining after 2658 seconds.
Therefore, the correct answer would be "B) 300,000 neutrons and 2,100,000 protons," since there would still be a significant number of neutrons remaining, along with the protons.