Question

Explain with example the term order of magnitude of a physical quantity

Answer 1

Order of Magnitude:

Definition: The order of magnitude of a physical quantity is its magnitude in powers of ten when that

physical quantity is expressed in powers of ten with one digit to the left of the decimal.

Note:

 Physical Quantity= M x 10n

,where M is a number greater than 1, but less than 10 and ‘n’ is a

positive or negative integer.

 If M < 3.2, the order of magnitude remains 10n

.

 If M ≥ 3.2 then the order of magnitude will become 10n+1

.

 While expressing the order of magnitude of a physical quantity, its unit must be mentioned.

Some examples of order of magnitude:

1) Mass of an electron = 9.1x10-31 kg

Here, since M = 9.1, which is > 3.2, so the order of magnitude changes to 10n+1

, i.e. order of

magnitude changes to 10-31+1 = 10-30kg

2) Charge on an electron = 1.6x10-19coulomb.

Here, since M = 1.6, which is < 3.2, so the order of magnitude stays as 10n

, i.e. Order of magnitude

=10-19coulomb.

3) Diameter of hydrogen atom = 1.02 x10-10m

Here, since M = 1.02, which is < 3.2, so the order of magnitude stays as 10-10m.

4) Radius of earth = 6.378x106m

Here the order of magnitude will be 106+1 = 107m.

5) Mass of earth = 5.983x1024kg

Here the order of magnitude will be 1024+1 = 1025kg