The sodium yellow doublet has wavelengths 5890 Å and λ Å and resolving power of a grating to resolve these lines is 982 , then value of λ is

Question

The sodium yellow doublet has wavelengths 5890 Å and λ Å and resolving power of a grating to resolve these lines is 982 , then value of λ is (A) 5896Å (B) 5880Å (C) 5869Å (D) 5876Å

Tardigrade Admin · Accepted Answer

Mean wavelength λ m=(5890 + λ /2) Wavelength difference dλ =λ -5890 Resolving power R of a grating R=(λ m/d λ )=((5890 + λ /2)/λ - 5890)=982 λ =5896 â«

Q. The sodium yellow doublet has wavelengths $5890 Å$ and $λ Å$ and resolving power of a grating to resolve these lines is $982$ , then value of $λ$ is

$5896Å$

$5880Å$

$5869Å$

$5876Å$

Mean wavelength $λ_{m} = \frac{5890 + λ}{2}$
Wavelength difference $d λ = λ - 5890$
Resolving power $R$ of a grating
$R = \frac{λ _{m}}{d λ} = \frac{\frac{5890 + λ}{2}}{λ - 5890} = 982$
$λ = 5896 Å$

Q. The sodium yellow doublet has wavelengths 5890Å and λÅ and resolving power of a grating to resolve these lines is 982 , then value of λ is

5896Å

5880Å

5869Å

5876Å