QUARTER FINAL STAGE 2026
St. Augustine's College: 47 points
St. John's Grammar School: 27 points
Aburi Girls' SHS: 25 points
QUESTION
A Geiger Muller counter reads $256$ counts after four seconds.
Give the count rate and the error in the count.
ANSWER: The count rate is $64$ counts per second, and the error in the count is $\pm16$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 256$
$t = 4\text{ s}$
$\text{Count rate} = \dfrac{256}{4}$
$\text{Count rate} = 64\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{256}$
$\text{Error} = \pm16\text{ counts}$
---
PRACTICE QUESTIONS
1. QUESTION: A Geiger Muller counter reads $169$ counts after thirteen seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $13$ counts per second, and the error in the count is $\pm13$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 169$
$t = 13\text{ s}$
$\text{Count rate} = \dfrac{169}{13}$
$\text{Count rate} = 13\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{169}$
$\text{Error} = \pm13\text{ counts}$
2. QUESTION: A Geiger Muller counter reads $196$ counts after seven seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $28$ counts per second, and the error in the count is $\pm14$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 196$
$t = 7\text{ s}$
$\text{Count rate} = \dfrac{196}{7}$
$\text{Count rate} = 28\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{196}$
$\text{Error} = \pm14\text{ counts}$
3. QUESTION: A Geiger Muller counter reads $225$ counts after five seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $45$ counts per second, and the error in the count is $\pm15$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 225$
$t = 5\text{ s}$
$\text{Count rate} = \dfrac{225}{5}$
$\text{Count rate} = 45\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{225}$
$\text{Error} = \pm15\text{ counts}$
4. QUESTION: A Geiger Muller counter reads $324$ counts after nine seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $36$ counts per second, and the error in the count is $\pm18$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 324$
$t = 9\text{ s}$
$\text{Count rate} = \dfrac{324}{9}$
$\text{Count rate} = 36\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{324}$
$\text{Error} = \pm18\text{ counts}$
5. QUESTION: A Geiger Muller counter reads $484$ counts after four seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $121$ counts per second, and the error in the count is $\pm22$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 484$
$t = 4\text{ s}$
$\text{Count rate} = \dfrac{484}{4}$
$\text{Count rate} = 121\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{484}$
$\text{Error} = \pm22\text{ counts}$
6. QUESTION: A Geiger Muller counter reads $576$ counts after eight seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $72$ counts per second, and the error in the count is $\pm24$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 576$
$t = 8\text{ s}$
$\text{Count rate} = \dfrac{576}{8}$
$\text{Count rate} = 72\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{576}$
$\text{Error} = \pm24\text{ counts}$
7. QUESTION: A Geiger Muller counter reads $625$ counts after five seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $125$ counts per second, and the error in the count is $\pm25$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 625$
$t = 5\text{ s}$
$\text{Count rate} = \dfrac{625}{5}$
$\text{Count rate} = 125\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{625}$
$\text{Error} = \pm25\text{ counts}$
8. QUESTION: A Geiger Muller counter reads $729$ counts after nine seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $81$ counts per second, and the error in the count is $\pm27$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 729$
$t = 9\text{ s}$
$\text{Count rate} = \dfrac{729}{9}$
$\text{Count rate} = 81\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{729}$
$\text{Error} = \pm27\text{ counts}$
9. QUESTION: A Geiger Muller counter reads $1296$ counts after six seconds. Give the count rate and the error in the count.
ANSWER: The count rate is $216$ counts per second, and the error in the count is $\pm36$ counts.
SOLUTION:
$\text{Count rate} = \dfrac{N}{t}$
$N = 1296$
$t = 6\text{ s}$
$\text{Count rate} = \dfrac{1296}{6}$
$\text{Count rate} = 216\text{ counts/s}$
$\text{Error} = \sqrt{N}$
$\text{Error} = \sqrt{1296}$
$\text{Error} = \pm36\text{ counts}$