Radiocarbon dating of Qur’anic manuscripts is a well-known practice and undertaken by many museums, universities and institutions alike. However, the same can not be said of Biblical manuscripts/papyri. Why this discrepancy ?
Some may claim that Paleography (the study of ancient writing systems to date historical manuscripts) is just the same as Radio-Carbon dating. From the onset, it should be obvious that a subjective science like Paleography can in no way stand up to rigorous, tested and proven science which Radiocarbon dating provides. Below is a discussion regarding the pitfalls of using paleography:
Taken from here: http://www.islamic-awareness.org/Quran/Text/Mss/radio.html
On the other hand, palaeography is a relative dating method which gives an order of events without giving an exact age. Thus, generally speaking, it cannot be used to pinpoint dates with high precision. Is palaeography a form of science? Commenting on the issues regarding the dating of inscriptions, William M. Schniedewind says:
The so-called science of paleography often relies on circular reasoning because there is insufficient data to draw precise conclusion about dating. Scholars also tend to oversimplify diachronic development, assuming models of simplicity rather than complexity.
In other words, palaeography can at best be termed as an inexact science, filled with uncertainties and imprecisions. It is not judicious to upscale palaeography for its reliability whilst, on the other hand, putting down radiocarbon dating for its alleged lack thereof. So, what is the general “rule of thumb” followed in dating manuscripts via palaeography?
This kind of precision dating defies the realities of scribal activity. The productive writing life of a scribe was probably around thirty or thirty-five years. Add to that the fact that the scribal profession was an apprenticed trade, with students learning a particular style from a teacher, and we find that a given hand may be present over multiple generations of scribes. Thus the “rule of thumb” should probably be to avoid dating a hand more precisely than a range of at least seventy or eighty years.
 W. M. Schniedewind, “Problems Of Paleographic Dating Of Inscriptions” in T. E. Levy, T. Higham (Eds.), The Bible And Radiocarbon Dating Archaeology, Text And Science, 2005, Equinox Publishing: London & Oakville, p. 405.
 B. Nongbri, “The Use And Abuse Of P52: Papyrological Pitfalls In The Dating Of The Fourth Gospel“, Harvard Theological Review, 2005, Volume 98, p. 32, footnote 27. The issue of uncertainty and imprecision has been long recognized as an issue in palaeography. For example, citing Eric Turner, Nongbri says ( p. 25, footnote 6):
Paleography is a last resort for dating… We would also do well to remember the standard rule of thumb for precision in paleographic dating, Turner writes, “For book hands, a period of 50 years is the least acceptable spread of time“.
 B. W. Griffin, “The Paleographical Dating Of P46“, 1996 (November). This paper was delivered to the Society of Biblical Literature, New Testament Textual Criticism Section, New Orleans. Its transcript can be found here (accessed on 5th June 2016). Griffin comments:
Until more rigorous methodologies are developed, it is difficult to construct a 95% confidence interval for NT manuscripts without allowing a century for an assigned date. If we use the 50-year period that is currently standard for the Oxyrhynchus series, then I would prefer AD 175-225 as the most probable date for P-46. But if we want a 95% confidence interval for P-46, then at present AD 150-250 is probably the narrowest range that we can use.