Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$$\stackrel{\circ }{A}$$. The radius of the atom in the excited state, in terms of Bohr radius a0 will be : (hc = 12500 eV$$\stackrel{\circ }{A}$$)

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $$\lambda$$. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

A particle of mass m moves in a circular orbit in a central potential field U(r) = {1 \over 2} kr2. If Bohr 's quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :

Consider the nuclear fission Ne20 $$\to$$ 2He4 + C12 Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 102 kg/m3 and specific heat of 2000 J kg–1 K–1 while liquid in B has density of 103 kg m–3 and specific heat of 4000 J kg–1 K–1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to : (Latent heat of vaporization of water = 2.10 × 106 J kg–1 and Latent heat of Fusion of water = 3.36 × 105 J kg–1)

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by :-

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to : [Boltzmann Constant kB = 1.38 × 10–23 J/K Avogadro Number NA = 6.02 × 1026 /kg Radius of Earth : 6.4 × 106 m Gravitational acceleration on Earth = 10ms–2]

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $$\overline{v}$$ , m is its mass and kB is Boltzmann constant, then its temperature will be :

Following figure shows two processes A and B for a gas. If $$\Delta$$QA and $$\Delta$$QB are the amount of heat absorbed by the system in two cases, and $$\Delta$$UA and $$\Delta$$UB are changes in internal energies, respectively, then :

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :

A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)

The specific heats, CP and CV of a gas of diatomic molecules, A, are given (in units of J mol–1 K–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$$\theta$$2' and '$$\theta$$1' respectively, ($$\theta$$2 > $$\theta$$1). The temperature at the interface is :-

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R = 8.31 J mol–1 K–1]

n moles of an ideal gas with constant volume heat capcity CV undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :

A 25 × 10–3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300K). The molecular diameter of O2, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O2 molecule ?

One mole of ideal gas passes through a process where pressure and volume obey the relation P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]. Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its volume changes form V0 to 2V0

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $$\Delta$$T. the heat required to produce the same change in temperature, at a constant pressure is :