Question:
Two fast moving particles X and Y are associated with de Broglie wavelengths 1 nm and 4 nm respectively. If mass of X is nine times the mass of Y, the ratio of kinetic energies of X and Y would be
Two fast moving particles X and Y are associated with de Broglie wavelengths 1 nm and 4 nm respectively. If mass of X is nine times the mass of Y, the ratio of kinetic energies of X and Y would be
Updated On: May 25, 2024
- 3 : 1
- 9 : 1
- 5 : 12
- 16 : 9
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The Correct Option is D
Solution and Explanation
Given :
\(\lambda=\frac{h}{mv}\)
Now, \(\frac{\lambda_2}{\lambda_1}=\frac{m_1v_1}{m_2v_2}=\frac{4}{1}\)
\(=\frac{9\times v_2}{1\times v_1}\)
\(\frac{v_2}{1}=\frac{9}{4}\)
K. E = 12 mv2
Now, Ratio of K.E is :
\(\frac{K.E_1}{K.E_2}=\frac{16}{9}\)
So, the correct option is (D) : 16 : 9.
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Concepts Used:
Dual Nature of Matter
- The concept of Dual Nature of Matter was proposed after various experiments supported both wave as well particle nature of light.
- The particle nature of matter came into the picture when Albert Einstein looked up to the experiment conducted by Max Planck and observed that the wavelength and intensity of matter have a certain impact on the ejected electrons. Experiments such as the photoelectric effect suggested that light has a particle nature, i.e. light travels in form of packets of energy (E = h\(\nu\))
- On the other hand, the wave nature of matter was hypothesised by De-Broglie and confirmed by the Davisson - German experiment.
- Therefore, it’s concluded that matter has dual nature; it means that it has both the properties of a particle as well as a wave.
