State two practical uses of photo cells.

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(b) (i) State two practical uses of photo cells.

Automatic street lighting: Photo cells detect ambient light levels and switch streetlights on at dusk and off at dawn.
Automatic door openers: They can detect the presence of a person by sensing an interruption in a light beam, triggering the door to open. Other uses include burglar alarms, light meters in cameras, and solar panels for electricity generation.

(b) (iii) A scientist uses a radioactive source with a half-life of $4 \, \text{hrs}$ as a clock. If the source initially emits 1220 particles per minute, what time interval has elapsed when he records 160 counts per minute?

Identify the given values.
Initial activity ( $N_0$ ) = 1220 counts/min
Final activity ( $N$ ) = 160 counts/min
Half-life ( $T_{1/2}$ ) = $4 \, \text{hrs}$
Use the radioactive decay formula to find the number of half-lives ( $n$ ).
The formula for radioactive decay is:
$N = N_0 \left(\frac{1}{2}\right)^n$
Substitute the given values:
$160 = 1220 \left(\frac{1}{2}\right)^n$
Divide both sides by 1220:
$\frac{160}{1220} = \left(\frac{1}{2}\right)^n$ $0.1311475 \approx \left(\frac{1}{2}\right)^n$
Take the natural logarithm of both sides:
$\ln(0.1311475) = n \ln\left(\frac{1}{2}\right)$ $-2.0316 \approx n (-0.6931)$
Solve for $n$ :
$n \approx \frac{-2.0316}{-0.6931}$ $n \approx 2.931$
Calculate the total time elapsed ( $t$ ).
The total time elapsed is the number of half-lives multiplied by the half-life period:
$t = n \times T_{1/2}$ $t \approx 2.931 \times 4 \, \text{hrs}$ $t \approx 11.724 \, \text{hrs}$
The time interval elapsed is $\boxed{\text{}11.72 \, \text{hrs}}$ .

State two practical uses of photo cells.

Step-by-step solution

Identify the given values.

Use the radioactive decay formula to find the number of half-lives ( $n$ ).

Calculate the total time elapsed ( $t$ ).

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More Physics Questions

State two practical uses of photo cells.

Step-by-step solution

Identify the given values.

Use the radioactive decay formula to find the number of half-lives (nnn).

Calculate the total time elapsed (ttt).

Still stuck on this one?

More Physics Questions

Use the radioactive decay formula to find the number of half-lives ( $n$ ).

Calculate the total time elapsed ( $t$ ).