Question

the average wavelength of light from a sodium lamp is 5893A. express it in metres and nanometers

Answer 1

1A°= 10^-10m
1nm =10^-9 m
In A° = 5893*10^-10m
In nm = 5893*10^-9 m

Answer 2

The given wavelength when expressed in meters and nanometers respectively will be $5.893 \times 10^{-7} \hspace{3} m$ and $589.3 \hspace{3} nm$.

Given,

The average wavelength of light from a sodium lamp = $5893 \AA$.

To find,

Express the given wavelength in meters and nanometers.

Solution,

Here, the average wavelength of the light from a sodium lamp is given to be

$5893 \AA$.

We can see that the given wavelength is in Angstrom ($\AA$).

Now, to convert it into meters and nanometers respectively, we have to use the following relations.

$1 \AA = 10^{-10} \hspace{3} m \hfill ...(1)$

$1 \AA = 10^{-1} \hspace{3} nm\\\implies 1 \AA = 0.1 \hspace{3} nm\hfill ...(2)$

Thus, $5893 \AA$ can be expressed in meters as follows.

Using (1),

$5893 \AA = 5893 \times 10^{-10} \hspace{3} m$

$\implies 5893 \AA = 5.893 \times 10^{-7} \hspace{3} m$.

Further, $5893 \AA$ can be expressed in nanometers as follows.

Using (2),

$5893 \AA=5893 \times 0.1 \hspace{3} nm$

$\implies 5893 \AA=589.3 \hspace{3} nm$.

Therefore, the given wavelength when expressed in meters and nanometers respectively will be $5.893 \times 10^{-7} \hspace{3} m$ and $589.3 \hspace{3} nm$.

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