There is no definitive answer to your question. The purpose of your study is to influence your scale development process, the structure you want to measure, the number of substances and many other factors that affect Cronbach Alfa.
There are some kind of urban legends about acceptable Cronbach Alfa values. For prior knowledge and realizing this interesting debate's popularity you can read the following article.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.463.428&rep=rep1&type=pdf
0.7 is a sufficient value for Nunally (1978) and this value is usually taken by researchers as criteria.
Thank you so much Prof. Taha Eser . Your insights are very helpful.
in the Philppne landscape and based on research practice, the acceptable margin is atleast high reliability for cronbach- altho the desired one is very high. Look into the scales so u can see the descriptive equivalent
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