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natta225 [31]
3 years ago
6

Each time you dumped the pennies, one half-life passed; it has been shown that the half-life for this radioactive isotope is 20

years
In the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery
It is shown that 95% of the nuclei have decayed
Approximately how long ago was the pottery made?
Physics
1 answer:
tresset_1 [31]3 years ago
3 0
The exponential decay function is shown as:

At = Ao*2^(-t/h)

Where:

At = Final amount
Ao = original amount
t = time
h = years for half-life to occur

We are not given the original and final amounts, but we are told that after the certain amount of time had passed, only 5% had remained. So if we were to isolate At and Ao in one side of the equation, such that: At/Ao = 0.05, we can solve for the missing variable, which is t.

Substituting:

<span>At/Ao = 2^(-t/h)
</span>0.05 = <span>2^(-t/20)
t = 86.44 years

Therefore, the pottery was made approximately 86.44 years ago.</span>
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Aloop of wire of area 71 cm^2 is placed with its plane parallel to a 16 mt magnetic field. the loop is then rotated so that its
kkurt [141]

Answer:

Approximately 1.62 × 10⁻⁴ V.

Explanation:

The average EMF in the coil is equal to

\displaystyle \frac{\text{Final Magnetic Flux} - \text{Initial Magnetic Flux}}{2},

Why does this formula work?

By Faraday's Law of Induction, the EMF \epsilon induced in a coil (one loop) is equal to the rate of change in the magnetic flux \Phi through the coil.

\displaystyle \epsilon(t) = \frac{d}{dt}(\Phi(t)).

Finding the average EMF in the coil is similar to finding the average velocity.

\displaystyle \text{Average}\; \epsilon = \frac{1}{t}\int_0^t \epsilon(t)\cdot dt.

However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:

\displaystyle \int_0^{t} \epsilon(t)\cdot dt = \int_0^{t} \frac{d}{dt}\Phi(t)\cdot dt = \Phi(t) - \Phi(0).

Hence the equation

\displaystyle \text{Average}\; \epsilon = \frac{1}{t}\int_0^t \epsilon(t)\cdot dt = \frac{\Phi(t)- \Phi(0)}{t}.

Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in \Phi(t) won't matter.

Apply this formula to this question. Note that \Phi, the magnetic flux through the coil, can be calculated with the equation

\Phi = B \cdot A \cdot N \; \sin{\theta}.

For this question,

  • B = \rm 16\; mT = 16\times 10^{-3}\; T is the strength of the magnetic field.
  • A = \rm 71\; cm^{2} = 71\times \left(10^{-2}\right)^2 \; m^{2} is the area of the coil.
  • N = 1 is the number of loops in the coil.
  • \theta is the angle between the field lines and the coil.
  • At \rm 0\;s, the field lines are parallel to the coil, \theta = 0^{\circ}.
  • At \rm 0.7\; s, the field lines are perpendicular to the coil, \displaystyle \theta = 90^{\circ}.

Initial flux: \Phi(0)= 0.

Final flux: \Phi(0.7) = \rm 1.1136\times 10^{-4}\; Wb.

Average EMF, which is the same as the average rate of change in flux:

\displaystyle \frac{\Phi(0.7) - \Phi(0)}{0.7} \approx\rm 1.62\times 10^{-4}\; V.

8 0
3 years ago
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