Question

this kinda of a long question, but all parts are connected. so, please explain !

The first quantitative description of the hydrogen spectrum was given by Johann Balmer, a Swiss school teacher, in 1885. By trial and error, he found that the correct wavelength ? of each line observed in the hydrogen spectrum was given by

1?=R(122?1n2),

where R is a constant, later called the Rydberg constant, and n may have the integer values 3, 4, 5, .... If ? is in meters, the numerical value of the Rydberg constant (determined from measurements of wavelengths) is R = 1.097×10⁷ m?1 .

Balmer knew only the four lines in the visible spectrum of hydrogen. Thus, the original formula was written for a limited set of values of n. However, as more techniques to detect other regions of the spectrum were developed, it became clear that Balmer's formula was valid for all values of n. The entire series of spectral lines predicted by Balmer's formula is now referred to as the Balmer series.

Part A

What is the wavelength of the line corresponding to n=4 in the Balmer series?

Part B

What is the wavelength of the line corresponding to n=5 in the Balmer series?

Part C

What is the smallest wavelength ?min in the Balmer's series?

Part D

What is the largest wavelength ?max in the Balmer series?

Part E

What is the smallest value of n for which the wavelength of a Balmer series line is smaller than 400nm, which is the lower limit for wavelengths in the visible spectrum?

Enter your answer as an integer.

Part F

If m=1, in what range are the wavelengths calculated from the generalized formula shown above?

If , in what range are the wavelengths calculated from the generalized formula shown above?

microwave (1 to 10?4m)

infrared (10?3 to 7×10?7m)

visible (7×10?7 to 4×10?7m)

ultraviolet (4×10?7 to 10?8m)

X rays (10?8 to 10?13m)

Part G

If m=3, in what range are wavelengths calculated from the generalized formula shown above?

If , in what range are wavelengths calculated from the generalized formula shown above?

microwave (1 to 10?4m)

infrared (10?3 to 7×10?7m)

visible (7×10?7 to 4×10?7m)

ultraviolet (4×10?7 to 10?8m)

X rays (10?8 to 10?13m

Answer 1

The wave number of the hydrogen spectra is, For Balmer series n1-2 and n2-3, 4,5, The wavelength corresponding to n 4 is calculated as follows 1.097 x10' λ = 4.862 x 10-7 m λ-486.2 nm The wavelength corresponding to n = 5 is calculated as follows =(1.097 × 10 m .)lat-15)2 (2)2 2 ( λ= 4.341×10-7 m λ= 434.1 nm

The smallest wavelength corresponds to n =00 is calculated as follows 1n ได้าไป = (1.097 x10' mı") min 3.646x10 m in 364.6 nm The longest wavelength corresponds to n -3 is calculated as follows ax = (1.097×107 m -1) 2-a)2 = 6.563×10-7 m 656.3 nm A,

The smallest value of n for which the wavelength of a Balmer series line is smaller than 400nm is calculated as follows 400 nm 400 x109 m 1.097x10 mi") RE-- 400x10-9 m n=673 If m -3 the range of wavelengths is calculated as follows 1.097 x10' m-i)| | to-=(1.097x10·m")| (3) (i λ= 8.204×10-7 m λ = 1.875 x 10-6 m This is belongs to infrared regioin

If = 1 the range of wavelengths is calculated as follows: (1.097 x 107 m-1)| = ( 1.097×10 m .)| λ=9.11x10-8 m λ-1.215x10" m This is belongs to ultraviolet region