Dual Nature of ...

After absorbing a slowly moving neutron of Mass $$m_N$$ (momentum $$\approx 0$$) a nucleus of mass M breaks into two nuclei of masses $$m_1$$ and $$5m_1$$ $$(6m_1=M+m_N)$$ respectively. If the de Broglie wavelength of he nucleus with mass $$m_1$$ is $$\lambda$$, the de Broglie wavelength of the nucleus will be.

For which of the following wave functions, does the heisenberg uncertainty relation read $$\Delta x\Delta {p_x} = h/2.$$

Particle having mass $$100 mg$$ is moving with a speed of $$200
m/s$$. The associated wavelength of the particle is $$( h = 6.626 \times
10^{-34} js)$$

Assume that a molecule is moving with the root mean square speed at temperature 300 K. The de Broglie wavelength of nitrogen molecule is (Atomic mass of nitrogen = 14.0076 u, h = $$6.63 \, \times \, 10^{-27} \, J \, s, \, k_B \, = \, 1.38 \, \times \, 10^{-23} J \, K^{-1}, \, 1 \, u \, = \, 1.66 \,. \times \, 10^{-27} \, kg)$$ 

If the momentum of an electron is changed by $$ \Delta p, $$ then the de-Brogile wavelength associated with it changes by $$0.05 \% $$ . The initial momentum of electron will be :

A surface irradiated with light of wavelength 480 nm gives out electrons with maximum velocity v m/s, the cut off wavelength being 600 nm. The same surface would release electrons with maximum velocity 2v m/s if it is irradiated by light of wavelength.

A proton and an$$\alpha - particle$$ accelerated through same voltage.The ratio of their de-broglie wavelength will be :

An electron is moving with velocity $$6.6 \times 10^3 mls.$$ The DE-Imbroglio wavelength associated with electron is $$(mass of electron = 9 \times 10^{-31}kg,$$ Plank's Constant = $$6.62 \times 10^{-34} J-S)$$

The de-Broglie wavelength $$(\lambda_{B})$$ associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state $$(\lambda_{G})$$ by

The value of $$\left( { n }_{ 2 }+{ n }_{ 1 } \right) $$ and $$\left( { n }_{ 2 }^{ 2 }-{ n }_{ 1 }^{ 2 } \right) $$ for $${ He }^{ + }$$ ion in atomic spectrum are 4 and 8 respectively. The wavelength of emitted photon when electron jump from $${ n }_{ 2 }$$ to $${ n }_{ 1 }$$ is: