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Chapter 37: Q. 1 (page 1081)

What are the wavelengths of spectral lines in the Balmer series with $n = 6, 8, a n d 10$ ?

Short Answer

Expert verified

The wavelengths with $n = 6, 8, 10$ are $410.31 n m, 389.03 n m a n d 379.92 n m$ respectively.

Step by step solution

01

Given information

We need to find the wavelengths of spectral lines in the Balmer series with $n = 6, 8, 10$ .

02

Explanation

Now the Rydberg formula for Balmer series is

$\frac{1}{2^{2}} - \frac{1}{n^{2}} = \frac{91.18 (n m)}{λ} λ = \frac{91.18 (n m)}{\frac{1}{2^{2}} - \frac{1}{n^{2}}}$

This is equation (1)

Now on substituting n value we get-

$F o r$ $n = 6$

$λ_{6} = \frac{91.18 (n m)}{\frac{1}{2^{2}} - \frac{1}{6^{2}}} λ_{6} = 410.31 n m F o r n = 8, λ_{8} = \frac{91.18 (n m)}{\frac{1}{2^{2}} - \frac{1}{8^{2}}} λ_{8} = 389.03 n m F o r n = 10, λ_{10} = \frac{91.18 (n m)}{\frac{1}{2^{2}} - \frac{1}{10^{2}}} λ_{10} = 379.92 n m$

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Most popular questions from this chapter

Event A occurs at spacetime coordinates (300 m, 2 s)

a. Event B occurs at spacetime coordinates (1200 m, 6 μs). Could A possibly be the cause of B? Explain.

b. Event C occurs at spacetime coordinates (2400 m, 8 μs). Could A possibly be the cause of C? Explain.

A brass plate at room temperature radiates 10 W of blackbody radiation. If the plate is cooled to –30°C, does the peak of maximum radiated intensity shift toward shorter wavelengths, shift toward longer wavelengths, or remain the same? Explain.

Rutherford studied alpha particles using the crossed-field technique Thomson had invented to study cathode rays. Assuming that $V_{a l p h a \approx} V_{c a t h o d e r a y}$ (which turns out to be true), would the deflection of an alpha particle by a magnetic field be larger than, smaller than, or the same as the deflection of a cathode-ray particle by the same field? Explain.

8. The current in a Crookes tube is $10 n A$ . How many electrons strike the face of the glass tube each second?

An electron in a cathode-ray beam passes between $2.5 - c m$ -long parallel-plate electrodes that are $5.0 m m$ apart. A $2.0 m T$ , $2.5 - c m$ -wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is $600 V .$

a. What is the electron’s speed?

b. If the potential difference between the plates is set to zero, what is the electron’s radius of curvature in the magnetic field?

See all solutions

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