Advertisements
Advertisements
प्रश्न
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3–t. After how many half-lives will the fraction be `1/243` of the original?
Advertisements
उत्तर
Given, t half-lives = 3–t
So, `1/243 = 3^-t`
⇒ `1/3^5 = 1/3^t` ...`[because 3 xx 3 xx 3 xx 3 xx 3 = 3^5 "and" a^-m = 1/a^m]`
On comparing both sides, we get
t = 5 half-lives
APPEARS IN
संबंधित प्रश्न
Express the given numbers in usual form.
3.02 × 10-6
Express the following numbers in standard form:
4 ÷ 100000
Write the following numbers in the usual form:
3 × 10−8
Write the following numbers in the usual form:
5.8 × 102
Express the following number in standard form.
0.000035
Express the following number in the usual form.
Divide 293 by 10,00,000 and express the result in standard form.
About 230 billion litres of water flows through a river each day. How many litres of water flows through that river in a week? How many litres of water flows through the river in an year? Write your answer in standard notation.
The given table shows the crop production of a State in the year 2008 and 2009. Observe the table given below and answer the given questions.
| Crop | 2008 Harvest (Hectare) |
Increase/Decrease (Hectare) in 2009 |
| Bajra | 1.4 × 103 | – 100 |
| Jowar | 1.7 × 106 | – 440,000 |
| Rice | 3.7 × 103 | – 100 |
| Wheat | 5.1 × 105 | + 190,000 |
- For which crop(s) did the production decrease?
- Write the production of all the crops in 2009 in their standard form.
- Assuming the same decrease in rice production each year as in 2009, how many acres will be harvested in 2015? Write in standard form.
Express the following in exponential form:
`(-625)/10000`
