A lead shielding (µ=1.19) is used to protection against a source of caesium 157 with dose rate of 0.11 R/h. emitted gamma radiation has a 0.6 Mev energy. If lead shielding thickness is 0.02 m, what will the permissible exposure time (stay time)?
According the calculated shielding thicknesses of Lead samples have been obtained in certain values in different gamma ray energies. For example, HVL value of Lead sample (d=11.9 gcm-1) for 500 kV radiation know as 3.6 mm and TVL value of lead in mentioned energy is 11.9 mm. If we consider your energy range as 0.6 MeV mean 600 keV.. So its mean you will need and HVL thickness of Lead more than 3.6 mm (maybe 4.5 around something)for HVL and around 12-13 mm for TVL.
Actually, stay time does not depend on shielding thickness but only on dose rate.
With a dose rate of 0,11 R/h, I understand 1,1 mSv/h, your will receive in one hour sligthly more than the maximum permissible dose for one year for general public.
If you mean that the dose rate is measured behind the shielding and want to evaluate the dose rate of the bare source, you have to know at least the distance between the measuring point and the shielding, provided that you can assume the source as a point one.
See for example IAEA safety standard for reference
It sounds like you have 0.11 R/hr, then you add 2 cm Pb shielding. So you will calculate a new dose rate after the shielding. Using 2 cm Pb, and Cs-137 gamma (0.66 MeV), I get a reduction of about 0.14: That is, the 0.11 rem/hr dose rate would be reduced to 0.14 of this, or about 0.016 mrem/hr. In order to get a stay time, you need an allowable dose. If you assume 0.1 Rem (100 mrem or 1 mSv), then your stay time would be 0.1 rem / 0.016 rem/hr, or about 6 hours.