10–15 second = ______.
1 femtosecond
Understanding Time Conversions: Seconds to Femtoseconds
The question asks to convert a value given in seconds, specifically $10^{-15}$ seconds, into another unit of time based on the provided options. These options represent different smaller units of time that are defined using standard SI prefixes applied to the base unit, the second.
Common SI Prefixes for Time Units
Let's look at the SI prefixes commonly used for very short time intervals and their corresponding power of 10 relative to the second:
- Nanosecond (ns): This prefix 'nano' represents $10^{-9}$. So, 1 nanosecond = $10^{-9}$ seconds.
- Picosecond (ps): This prefix 'pico' represents $10^{-12}$. So, 1 picosecond = $10^{-12}$ seconds.
- Femtosecond (fs): This prefix 'femto' represents $10^{-15}$. So, 1 femtosecond = $10^{-15}$ seconds.
- Attosecond (as): This prefix 'atto' represents $10^{-18}$. So, 1 attosecond = $10^{-18}$ seconds.
Converting $10^{-15}$ seconds
We are given the value $10^{-15}$ seconds. We need to find which of the given units is equivalent to this value.
Comparing the given value with the definitions above:
- $10^{-15}$ seconds vs 1 nanosecond ($10^{-9}$ seconds): Not equal.
- $10^{-15}$ seconds vs 1 picosecond ($10^{-12}$ seconds): Not equal.
- $10^{-15}$ seconds vs 1 femtosecond ($10^{-15}$ seconds): They are equal.
- $10^{-15}$ seconds vs 1 attosecond ($10^{-18}$ seconds): Not equal.
Therefore, $10^{-15}$ seconds is equal to 1 femtosecond.
Analysing the Options
Let's examine each option based on our conversion:
- 1 Attosecond: This is $10^{-18}$ seconds. This does not match $10^{-15}$ seconds.
- 1 femtosecond: This is $10^{-15}$ seconds. This exactly matches the value given in the question.
- 1 picosecond: This is $10^{-12}$ seconds. This does not match $10^{-15}$ seconds.
- 1 nanosecond: This is $10^{-9}$ seconds. This does not match $10^{-15}$ seconds.
Based on the analysis, the value $10^{-15}$ seconds is equivalent to 1 femtosecond.
| Unit | SI Prefix | Power of 10 | Value in Seconds |
|---|---|---|---|
| Second (s) | - | $10^0$ | 1 s |
| Millisecond (ms) | milli | $10^{-3}$ | $0.001$ s |
| Microsecond (µs) | micro | $10^{-6}$ | $0.000001$ s |
| Nanosecond (ns) | nano | $10^{-9}$ | $10^{-9}$ s |
| Picosecond (ps) | pico | $10^{-12}$ | $10^{-12}$ s |
| Femtosecond (fs) | femto | $10^{-15}$ | $10^{-15}$ s |
| Attosecond (as) | atto | $10^{-18}$ | $10^{-18}$ s |
| Zeptosecond (zs) | zepto | $10^{-21}$ | $10^{-21}$ s |
| Yoctosecond (ys) | yocto | $10^{-24}$ | $10^{-24}$ s |
Revision Table: Time Unit Equivalents
| Unit | Equivalent in Seconds |
|---|---|
| 1 Nanosecond | $10^{-9}$ s |
| 1 Picosecond | $10^{-12}$ s |
| 1 Femtosecond | $10^{-15}$ s |
| 1 Attosecond | $10^{-18}$ s |
Additional Information on SI Prefixes
SI prefixes are standard multipliers that are used with SI units (like the second, meter, gram, etc.) to denote multiples or submultiples of the unit. They make it easier to express very large or very small numbers.
Some common SI prefixes and their factors:
- kilo (k) - $10^3$
- mega (M) - $10^6$
- giga (G) - $10^9$
- tera (T) - $10^{12}$
- peta (P) - $10^{15}$
- exa (E) - $10^{18}$
- zetta (Z) - $10^{21}$
- yotta (Y) - $10^{24}$
- milli (m) - $10^{-3}$
- micro (µ) - $10^{-6}$
- nano (n) - $10^{-9}$
- pico (p) - $10^{-12}$
- femto (f) - $10^{-15}$
- atto (a) - $10^{-18}$
- zepto (z) - $10^{-21}$
- yocto (y) - $10^{-24}$
Understanding these prefixes is crucial for working with units in physics, chemistry, engineering, and many other scientific fields.
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1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
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If the sum S is divided by 60, what is the remainder ?
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Four prime numbers are arranged in ascending order. The product of the first three numbers is 255 and that of the last three is 1955. The largest prime number is:
