Dual Nature of Radiation

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

The work function of a substance is $4.0$ $eV.$ The longest wavelength of light that can cause photo-electron emission from this substance is approximately.

An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths? (m_p = 1.00727u m_e = 0.00055u)

A parallel beam of light of wavelength $900 \mathrm{~nm}$ and intensity $100 \,\mathrm{Wm}^{-2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1 \mathrm{~cm}^{2}$ area perpendicular to the beam in one second is :

The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :

This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement 1 : Davisson - Germer experiment established the wave nature of electrons. Statement 2 : If electrons have wave nature, they can interfere and show diffraction.

The speed of electrons in a scanning electron microscope is 1 $\times$ 10⁷ ms⁻¹. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of :

Given below are two statements : Statement I : Davisson-Germer experiment establishes the wave nature of electrons. Statement II : If electrons have wave nature, they can interfere and show diffraction. In the light of the above statements choose the correct answer from the option given below :

A nucleus A, with a finite de-broglie wavelength $\lambda$_A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths $\lambda$_B and $\lambda$_C of B and C are respectively :

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$\lambda$_x' and '$\lambda$_y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R Assertion A : The beam of electrons show wave nature and exhibit interference and diffraction. Reason R : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements, choose the most appropriate answer from the options given below :

Formation of covalent bonds in compounds exhibits

If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\lambda _A}$ to ${\lambda _B}$ after the collision is:

Particle A of mass m_A = ${m \over 2}$ moving along the x-axis with velocity v₀ collides elastically with another particle B at rest having mass m_B = ${m \over 3}$. If both particles move along the x-axis after the collision, the change $\Delta$$\lambda$ in de-Broglie wavlength of particle A, in terms of its de-Broglie wavelength ($\lambda$₀) before collision is :

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are ${\lambda _1}$ and ${\lambda _2},$ their de Broglie wavelength in the frame of reference attached to their center of masses :

If the de Broglie wavelengths associated with a proton and an $\alpha$-particle are equal, then the ratio of velocities of the proton and the $\alpha$-particle will be :