Question #80604
In the determination of wavelength of light from a sodium lamp using Michelson's interferometer ,the following values were obtained in (nm) 587.2,590.3,584.7,591.3,586.5,587.8,593.9,588.1,600.1& 592.0.calculate
a. the mean wavelength
b. the standard deviation
c. the mean standard deviation
a. the mean wavelength
b. the standard deviation
c. the mean standard deviation
Expert's answer
a.
∑▒x=587.2+590.3+584.7+591.3+586.5+587.8+593.9+588.1+600.1+ 592.0=5901.9
The mean wavelength:
5901.9/10=590.2 nm.
b.
∑▒x^2 =〖587.2〗^2+〖590.3〗^2+〖584.7〗^2+〖591.3〗^2+〖586.5〗^2+〖587.8〗^2+〖593.9〗^2+〖588.1〗^2+〖600.1〗^2+ 〖592.0〗^2=3483421.63
The standard deviation is
√((3483421.63-(5901.9)^2/10)/(10-1))=4.46 nm.
∑▒x=587.2+590.3+584.7+591.3+586.5+587.8+593.9+588.1+600.1+ 592.0=5901.9
The mean wavelength:
5901.9/10=590.2 nm.
b.
∑▒x^2 =〖587.2〗^2+〖590.3〗^2+〖584.7〗^2+〖591.3〗^2+〖586.5〗^2+〖587.8〗^2+〖593.9〗^2+〖588.1〗^2+〖600.1〗^2+ 〖592.0〗^2=3483421.63
The standard deviation is
√((3483421.63-(5901.9)^2/10)/(10-1))=4.46 nm.
